{"id":934,"date":"2019-06-10T13:04:20","date_gmt":"2019-06-10T17:04:20","guid":{"rendered":"https:\/\/pressbooks.library.ryerson.ca\/ohsmath\/?post_type=chapter&p=934"},"modified":"2020-09-15T08:25:57","modified_gmt":"2020-09-15T12:25:57","slug":"unit-4-measurement","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.torontomu.ca\/ohsmath\/chapter\/unit-4-measurement\/","title":{"raw":"1.3. Measurement Systems","rendered":"1.3. Measurement Systems"},"content":{"raw":"
\r\n\r\n[Latexpage]\r\n\r\n<\/div>\r\n

Measurement Systems<\/strong><\/h1>\r\nMetric system (SI \u2013 international system of units):<\/strong> the most widely used system of measurement in the world. It is based on the basic units of meter, kilogram, second, etc.\r\n\r\nSI common units:<\/strong>\r\n\r\n\r\n\r\n
Quantity<\/strong><\/td>\r\nUnit <\/strong><\/td>\r\nUnit<\/strong> symbol<\/strong><\/td>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Length<\/strong><\/td>\r\nmeter<\/td>\r\nm<\/td>\r\n<\/tr>\r\n
Mass (or weight)<\/strong><\/td>\r\ngram<\/td>\r\nkg<\/td>\r\n<\/tr>\r\n
Volume<\/strong><\/td>\r\nlitre<\/td>\r\nL<\/td>\r\n<\/tr>\r\n
Time<\/strong><\/td>\r\nsecond<\/td>\r\ns<\/td>\r\n<\/tr>\r\n
Temperature<\/strong><\/td>\r\ndegree (Celsius)<\/td>\r\n\u00b0C<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\nMetric prefixes (SI prefixes)<\/strong>: <\/strong>\u00a0large and small numbers are made by adding SI prefixes, which is based on multiples of 10.\r\n\r\nMetric conversion table<\/strong>:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Pref<\/strong>ix<\/strong><\/td>\r\nSymbol <\/strong>(abbreviation)<\/strong><\/td>\r\nPower of 10<\/strong><\/td>\r\nMultiple value<\/strong><\/td>\r\nExample<\/strong><\/td>\r\n<\/tr>\r\n
mega<\/td>\r\nM<\/td>\r\n106<\/sup><\/td>\r\n1,000,000<\/td>\r\n1 Mm = 1,000,000 m<\/td>\r\n<\/tr>\r\n
kilo-<\/td>\r\nk<\/td>\r\n103<\/sup><\/td>\r\n1,000<\/td>\r\n1 km = 1,000 m<\/td>\r\n<\/tr>\r\n
hecto-<\/td>\r\nh<\/td>\r\n102<\/sup><\/td>\r\n100<\/td>\r\n1 hm = 100 m<\/td>\r\n<\/tr>\r\n
deka-<\/td>\r\nda<\/td>\r\n101<\/sup><\/td>\r\n10<\/td>\r\n1 dam = 10 m<\/td>\r\n<\/tr>\r\n
meter\/gram\/litre<\/strong><\/td>\r\n<\/td>\r\n1<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
deci-<\/td>\r\nd<\/td>\r\n10-1<\/sup><\/td>\r\n0.1<\/td>\r\n1 m = 10 dm<\/td>\r\n<\/tr>\r\n
centi-<\/td>\r\nc<\/td>\r\n10-2<\/sup><\/td>\r\n0.01<\/td>\r\n1 m = 100 cm<\/td>\r\n<\/tr>\r\n
milli-<\/td>\r\nm<\/td>\r\n10-3<\/sup><\/td>\r\n0.001<\/td>\r\n1 m = 1,000 mm<\/td>\r\n<\/tr>\r\n
micro<\/td>\r\n\u00b5<\/td>\r\n10-6<\/sup><\/td>\r\n0.000 001<\/td>\r\n1 m = 1,000,000 \u00b5m<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\nMetric prefix for length, weight and volume<\/strong>:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Prefix<\/strong><\/td>\r\nLength<\/strong> (m - meter)<\/strong><\/td>\r\nWeight<\/strong> (g - gram)<\/strong><\/td>\r\nLiquid volume<\/strong> (L - litre)<\/strong><\/td>\r\n<\/tr>\r\n
mega (M)<\/td>\r\nMm\u00a0 \u00a0 (Megameter)<\/td>\r\nMg\u00a0 \u00a0 (Megagram)<\/td>\r\nML\u00a0 \u00a0 \u00a0(Megalitre)<\/td>\r\n<\/tr>\r\n
kilo (k)<\/td>\r\nkm\u00a0 \u00a0 \u00a0 (Kilometer)<\/td>\r\nkg\u00a0 \u00a0 \u00a0 (Kilogram)<\/td>\r\nkL\u00a0 \u00a0 \u00a0 (Kilolitre)<\/td>\r\n<\/tr>\r\n
hecto (h)<\/td>\r\nhm\u00a0 \u00a0 \u00a0 (hectometer)<\/td>\r\nhg\u00a0 \u00a0 \u00a0 (hectogram)<\/td>\r\nhL\u00a0 \u00a0 \u00a0 (hectolitre)<\/td>\r\n<\/tr>\r\n
deka (da)<\/td>\r\ndam\u00a0 \u00a0 (dekameter)<\/td>\r\ndag\u00a0 \u00a0 (dekagram)<\/td>\r\ndaL\u00a0 \u00a0 (dekalitre)<\/td>\r\n<\/tr>\r\n
meter\/gram\/litre<\/strong><\/td>\r\nm\u00a0 \u00a0 \u00a0 \u00a0 (meter)<\/td>\r\ng\u00a0 \u00a0 \u00a0 \u00a0 (gram)<\/td>\r\nL\u00a0 \u00a0 \u00a0 \u00a0 (litre)<\/td>\r\n<\/tr>\r\n
deci (d)<\/td>\r\ndm\u00a0 \u00a0 \u00a0 (decimeter)<\/td>\r\ndg\u00a0 \u00a0 \u00a0 (decigram)<\/td>\r\ndL\u00a0 \u00a0 \u00a0 (decilitre)<\/td>\r\n<\/tr>\r\n
centi (c)<\/td>\r\ncm\u00a0 \u00a0 \u00a0 (centimeter)<\/td>\r\ncg\u00a0 \u00a0 \u00a0 (centigram)<\/td>\r\ncL\u00a0 \u00a0 \u00a0 (centilitre)<\/td>\r\n<\/tr>\r\n
milli (m)<\/td>\r\nmm\u00a0 \u00a0 \u00a0(millimeter)<\/td>\r\nmg\u00a0 \u00a0 \u00a0(milligram)<\/td>\r\nmL\u00a0 \u00a0 \u00a0(millilitre)<\/td>\r\n<\/tr>\r\n
micro (\u00b5)<\/td>\r\n\u00b5m\u00a0 \u00a0 \u00a0(micrometer)<\/td>\r\n\u00b5g\u00a0 \u00a0 \u00a0(microgram)<\/td>\r\n\u00b5L\u00a0 \u00a0 \u00a0(microlitre)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\nSteps for metric conversion:<\/strong>\r\n
    \r\n \t
  • Identify the number of places to move the decimal point.<\/li>\r\n<\/ul>\r\n

    - Convert a smaller<\/em><\/strong> unit to<\/em><\/strong> a larger<\/em><\/strong> unit: move the decimal point to the left<\/em><\/strong>.<\/p>\r\n

    - Convert a larger<\/em><\/strong> unit to<\/em><\/strong> a smaller<\/em><\/strong> unit:\u00a0 move the decimal point to the right<\/em><\/strong>.<\/p>\r\n\r\n

    \r\n

    Example 1.3.1<\/p>\r\n\r\n<\/header>\r\n

    \r\n\r\n326 mm = (?) m\r\n
      \r\n \t
    • Identify mm (millimeters<\/em>) and m (meters<\/em>) on the conversion table.<\/li>\r\n<\/ul>\r\n

      Count places from mm to m:\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3 places left<\/p>\r\n\r\n

      \"\"<\/div>\r\n
        \r\n \t
      • Move 3 decimal places. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(1 m = 1000 mm)<\/li>\r\n<\/ul>\r\n

        Convert a smaller unit (mm) to a larger (m) unit: move the decimal point to the left.<\/p>\r\n\r\n\r\n\r\n\r\n
        326. mm = 0.326 m<\/td>\r\nMove the decimal point three places to the left (326 = 326.<\/strong>).<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n \r\n
        \r\n

        Example 1.3.2<\/p>\r\n\r\n<\/header>\r\n

        \r\n\r\n4.675 hg = (?) g\r\n
          \r\n \t
        • Identify hg (hectograms<\/em>) and g (grams<\/em>) on the conversion table.<\/li>\r\n<\/ul>\r\n

          Count places from hg to g:\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2 places right<\/p>\r\n\r\n

          \"\"<\/div>\r\n
            \r\n \t
          • Move 2 decimal places. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(1 hg = 100 g)<\/li>\r\n<\/ul>\r\n

            Convert a larger unit (hg) to a smaller (g) unit:\u00a0 move the decimal point to the right.<\/p>\r\n\r\n\r\n\r\n\r\n
            4.765 hg = 476.5 g<\/td>\r\nMove the decimal point two places to the right.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
            \r\n

            <\/h1>\r\n

            The Unit Factor Method<\/strong><\/h1>\r\n<\/div>\r\nConvert units using the unit factor method (or the factor-label method)\u00a0<\/strong>\r\n
              \r\n \t
            • Write the original term as a fraction (over 1).<\/li>\r\n<\/ul>\r\n
              Example:\u00a0 10g can be written as $\\frac{10g}{1}$<\/div>\r\n
                \r\n \t
              • Write the conversion formula as a fraction $\\frac{1}{(\\;)}$ or $\\frac{(\\;)}{1}$.<\/li>\r\n<\/ul>\r\n
                Example:\u00a0 1m = 100 cm can be written as $\\frac{1m}{(100cm)}$ or $\\frac{(100cm)}{1m}$<\/div>\r\n
                  \r\n \t
                • Put the desired or unknown unit on the top.<\/li>\r\n \t
                • Multiply the original term by $\\frac{1}{(\\;)}$ or $\\frac{(\\;)}{1}$. (Cancel out the same units).<\/li>\r\n<\/ul>\r\n \r\n
                  \r\n

                  Example 1.3.3<\/p>\r\n\r\n<\/header>\r\n

                  \r\n\r\n1200 g = (?) kg\r\n
                    \r\n \t
                  • Write the original term (the left side) as a fraction: $1200 g = \\frac{1200 g}{1}$<\/li>\r\n \t
                  • Write the conversion formula as a fraction. 1 kg = 1000 g: $\\frac{1 kg}{(1000 g)}$<\/li>\r\n \t
                  • \u201ckg\u201d is the desired unit.<\/li>\r\n<\/ul>\r\n
                      \r\n \t
                    • Multiply: $1200 g = \\frac{1200 \\bcancel{g}}{1} \\cdot \\frac{1 kg}{(1000 \\bcancel{g})}$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 The units \u201cg\u201d cancel out.<\/li>\r\n<\/ul>\r\n

                      $= \\frac{1200 kg}{1000}$<\/p>\r\n

                      $= 1.2 kg$<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n \r\n

                      \r\n

                      Example 1.3.4<\/p>\r\n\r\n<\/header>\r\n

                      \r\n\r\n30 cm = (?) mm\r\n
                        \r\n \t
                      • Write the original term (the left side) as a fraction: $30 cm = \\frac{30 cm}{1}$<\/li>\r\n \t
                      • Write the conversion formula as a fraction. 1 cm = 10 mm: $\\frac{(10 mm)}{1cm}$<\/li>\r\n<\/ul>\r\n

                        \u201cmm\u201d is the desired unit.<\/p>\r\n\r\n

                          \r\n \t
                        • Multiply: $30 cm = \\frac{30 \\bcancel{cm}}{(1 mm)} \\cdot \\frac{(10 mm)}{1 \\bcancel{cm}}$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0The units \u201ccm\u201d cancel out.<\/li>\r\n<\/ul>\r\n

                          $= \\frac{(30)(10) mm}{1}$<\/p>\r\n

                          $= 300 mm$<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n \r\n\r\nAdding and subtracting SI measurements:<\/strong>\r\n

                          \r\n

                          Example 1.3.5<\/p>\r\n\r\n<\/header>\r\n

                          \r\n\r\nCombine after converting to the same unit.\r\n\r\n\r\n\r\n\r\n\r\n
                          3 m<\/td>\r\n<\/td>\r\n3000 mm<\/td>\r\n1 m = 1,000 mm<\/td>\r\n<\/tr>\r\n
                          \u2013\u00a0 \u00a02000 mm<\/span><\/td>\r\n--------><\/td>\r\n\u2013\u00a0 \u00a02000 mm<\/span><\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          <\/td>\r\n<\/td>\r\n1000 mm<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n
                          25 kg<\/td>\r\n<\/td>\r\n25000 g<\/td>\r\n1 kg = 1000 g<\/td>\r\n<\/tr>\r\n
                          +\u00a0 \u00a0 \u00a04 g<\/span><\/td>\r\n--------><\/td>\r\n+\u00a0 \u00a0 \u00a0 4 g<\/span><\/td>\r\n<\/td>\r\n<\/tr>\r\n
                          <\/td>\r\n<\/td>\r\n25004 g<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n \r\n
                          \r\n

                          The Relationship between mL<\/em>, g<\/em> and cm3<\/sup><\/strong><\/h1>\r\n<\/div>\r\nHow are mL, g, and cm3<\/sup> related?<\/strong>\r\n\r\n\"\"\r\n
                            \r\n \t
                          • A cube takes up 1 cm3<\/sup> of space (1 cm \u00d7 1 cm \u00d7 1 cm = 1cm3<\/sup>).<\/li>\r\n \t
                          • A cube holds 1 mL of water and has a mass of 1 gram at 4\u00b0C.<\/li>\r\n \t
                          • 1 cm3<\/sup> = 1 mL = 1 g<\/li>\r\n<\/ul>\r\n \r\n
                            \r\n

                            Example 1.3.6<\/p>\r\n\r\n<\/header>\r\n

                            \r\n\r\nConvert.\r\n\r\n\r\n\r\n\r\n
                            1) <\/strong>16cm3<\/sup> = ( ? ) g<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                            16cm3<\/sup> = 16 g<\/td>\r\n1 cm3<\/sup> = 1 g<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n
                            2) <\/strong>9 L = ( ? ) cm3<\/sup><\/td>\r\n<\/td>\r\n<\/tr>\r\n
                            9 L = 9000 mL<\/td>\r\n1 L = 1,000 mL<\/td>\r\n<\/tr>\r\n
                            = 9000 cm3<\/sup><\/td>\r\n1 mL = 1 cm3<\/sup><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n
                            3) <\/strong>35 cm3<\/sup> = (?) cL<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                            35cm3<\/sup> = 35 mL<\/td>\r\n1 cm3<\/sup> = 1 mL<\/td>\r\n<\/tr>\r\n
                            = 3.5 cL<\/td>\r\nmove 1 decimal place left.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                            4) <\/strong>450 kg = (?) L<\/td>\r\n<\/td>\r\n<\/tr>\r\n
                            450 kg = 450,000 g<\/td>\r\n1 kg = 1,000 g<\/td>\r\n<\/tr>\r\n
                            = 450,000 mL<\/td>\r\n1 g = 1 mL<\/td>\r\n<\/tr>\r\n
                            = 450 L<\/td>\r\n1 L = 1,000 mL<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n \r\n
                            \r\n

                            Example 1.3.7<\/p>\r\n\r\n<\/header>\r\n

                            \r\n\r\nA swimming pool measures 10 m by 8 m by 2 m. How many kilolitres<\/em><\/strong> of water will it hold?\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                            V<\/em> = w<\/em> l h <\/em>= (8m) (10m) (2m) = 160 m3<\/sup><\/td>\r\n160 m3<\/sup> = ( ? ) kL<\/td>\r\n<\/tr>\r\n
                            160m3<\/sup> = 160,000,000 cm3<\/sup><\/td>\r\n1 m = 100 cm, 3<\/strong> \u00d7 2 = 6, move 6 places right for volume.<\/td>\r\n<\/tr>\r\n
                            160,000,000 cm3<\/sup> = 160,000,000 mL<\/td>\r\n1 mL = 1 cm3<\/sup><\/td>\r\n<\/tr>\r\n
                            160,000,000 mL = 160 kL<\/td>\r\n1 kL = 1,000,000 mL<\/td>\r\n<\/tr>\r\n
                            160 m3<\/sup> = 160 kL<\/td>\r\nThe swimming pool will hold 160 kL of water.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
                            \r\n\r\n \r\n

                            Practice questions<\/strong><\/h1>\r\n1.<\/strong> Convert each of the following measurements<\/span>:\r\n\r\n<\/div>\r\n

                            a. <\/strong>439 mm = ( ? ) m<\/p>\r\n

                            b. <\/strong>48.3 mL = ( ? ) kL<\/p>\r\n

                            c. <\/strong>7230 g = ( ? ) kg<\/p>\r\n

                            d. <\/strong>52 cm = ( ? ) mm<\/p>\r\n3.<\/strong> Combine:\r\n

                            a. <\/strong>7 m \u2013 3000 mm = ( ? ) mm<\/p>\r\n

                            b. <\/strong>63 kg + 6 g = ( ? ) g<\/p>\r\n4.<\/strong> Complete:<\/span>\r\n

                            a. <\/strong>38 cm3<\/sup> = (\u00a0 \u00a0 \u00a0 \u00a0) g<\/p>\r\n

                            b. <\/strong>5 L = (\u00a0 \u00a0 \u00a0 \u00a0) cm3<\/sup><\/p>\r\n

                            c. <\/strong>18 L of water has a volume of ___________ cm3<\/sup> .<\/p>\r\n

                            d. <\/strong>A water tank measures 45 cm by 35 cm by 25 cm. How many kilolitres of water will it hold?<\/p>\r\n \r\n\r\n ","rendered":"

                            \n<\/div>\n

                            Measurement Systems<\/strong><\/h1>\n

                            Metric system (SI \u2013 international system of units):<\/strong> the most widely used system of measurement in the world. It is based on the basic units of meter, kilogram, second, etc.<\/p>\n

                            SI common units:<\/strong><\/p>\n\n\n\n
                            Quantity<\/strong><\/td>\nUnit <\/strong><\/td>\nUnit<\/strong> symbol<\/strong><\/td>\n<\/tr>\n<\/thead>\n<\/table>\n\n\n\n\n\n\n\n
                            Length<\/strong><\/td>\nmeter<\/td>\nm<\/td>\n<\/tr>\n
                            Mass (or weight)<\/strong><\/td>\ngram<\/td>\nkg<\/td>\n<\/tr>\n
                            Volume<\/strong><\/td>\nlitre<\/td>\nL<\/td>\n<\/tr>\n
                            Time<\/strong><\/td>\nsecond<\/td>\ns<\/td>\n<\/tr>\n
                            Temperature<\/strong><\/td>\ndegree (Celsius)<\/td>\n\u00b0C<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                             <\/p>\n

                            Metric prefixes (SI prefixes)<\/strong>: <\/strong>\u00a0large and small numbers are made by adding SI prefixes, which is based on multiples of 10.<\/p>\n

                            Metric conversion table<\/strong>:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
                            Pref<\/strong>ix<\/strong><\/td>\nSymbol <\/strong>(abbreviation)<\/strong><\/td>\nPower of 10<\/strong><\/td>\nMultiple value<\/strong><\/td>\nExample<\/strong><\/td>\n<\/tr>\n
                            mega<\/td>\nM<\/td>\n106<\/sup><\/td>\n1,000,000<\/td>\n1 Mm = 1,000,000 m<\/td>\n<\/tr>\n
                            kilo-<\/td>\nk<\/td>\n103<\/sup><\/td>\n1,000<\/td>\n1 km = 1,000 m<\/td>\n<\/tr>\n
                            hecto-<\/td>\nh<\/td>\n102<\/sup><\/td>\n100<\/td>\n1 hm = 100 m<\/td>\n<\/tr>\n
                            deka-<\/td>\nda<\/td>\n101<\/sup><\/td>\n10<\/td>\n1 dam = 10 m<\/td>\n<\/tr>\n
                            meter\/gram\/litre<\/strong><\/td>\n<\/td>\n1<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
                            deci-<\/td>\nd<\/td>\n10-1<\/sup><\/td>\n0.1<\/td>\n1 m = 10 dm<\/td>\n<\/tr>\n
                            centi-<\/td>\nc<\/td>\n10-2<\/sup><\/td>\n0.01<\/td>\n1 m = 100 cm<\/td>\n<\/tr>\n
                            milli-<\/td>\nm<\/td>\n10-3<\/sup><\/td>\n0.001<\/td>\n1 m = 1,000 mm<\/td>\n<\/tr>\n
                            micro<\/td>\n\u00b5<\/td>\n10-6<\/sup><\/td>\n0.000 001<\/td>\n1 m = 1,000,000 \u00b5m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                             <\/p>\n

                            Metric prefix for length, weight and volume<\/strong>:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
                            Prefix<\/strong><\/td>\nLength<\/strong> (m – meter)<\/strong><\/td>\nWeight<\/strong> (g – gram)<\/strong><\/td>\nLiquid volume<\/strong> (L – litre)<\/strong><\/td>\n<\/tr>\n
                            mega (M)<\/td>\nMm\u00a0 \u00a0 (Megameter)<\/td>\nMg\u00a0 \u00a0 (Megagram)<\/td>\nML\u00a0 \u00a0 \u00a0(Megalitre)<\/td>\n<\/tr>\n
                            kilo (k)<\/td>\nkm\u00a0 \u00a0 \u00a0 (Kilometer)<\/td>\nkg\u00a0 \u00a0 \u00a0 (Kilogram)<\/td>\nkL\u00a0 \u00a0 \u00a0 (Kilolitre)<\/td>\n<\/tr>\n
                            hecto (h)<\/td>\nhm\u00a0 \u00a0 \u00a0 (hectometer)<\/td>\nhg\u00a0 \u00a0 \u00a0 (hectogram)<\/td>\nhL\u00a0 \u00a0 \u00a0 (hectolitre)<\/td>\n<\/tr>\n
                            deka (da)<\/td>\ndam\u00a0 \u00a0 (dekameter)<\/td>\ndag\u00a0 \u00a0 (dekagram)<\/td>\ndaL\u00a0 \u00a0 (dekalitre)<\/td>\n<\/tr>\n
                            meter\/gram\/litre<\/strong><\/td>\nm\u00a0 \u00a0 \u00a0 \u00a0 (meter)<\/td>\ng\u00a0 \u00a0 \u00a0 \u00a0 (gram)<\/td>\nL\u00a0 \u00a0 \u00a0 \u00a0 (litre)<\/td>\n<\/tr>\n
                            deci (d)<\/td>\ndm\u00a0 \u00a0 \u00a0 (decimeter)<\/td>\ndg\u00a0 \u00a0 \u00a0 (decigram)<\/td>\ndL\u00a0 \u00a0 \u00a0 (decilitre)<\/td>\n<\/tr>\n
                            centi (c)<\/td>\ncm\u00a0 \u00a0 \u00a0 (centimeter)<\/td>\ncg\u00a0 \u00a0 \u00a0 (centigram)<\/td>\ncL\u00a0 \u00a0 \u00a0 (centilitre)<\/td>\n<\/tr>\n
                            milli (m)<\/td>\nmm\u00a0 \u00a0 \u00a0(millimeter)<\/td>\nmg\u00a0 \u00a0 \u00a0(milligram)<\/td>\nmL\u00a0 \u00a0 \u00a0(millilitre)<\/td>\n<\/tr>\n
                            micro (\u00b5)<\/td>\n\u00b5m\u00a0 \u00a0 \u00a0(micrometer)<\/td>\n\u00b5g\u00a0 \u00a0 \u00a0(microgram)<\/td>\n\u00b5L\u00a0 \u00a0 \u00a0(microlitre)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                             <\/p>\n

                            Steps for metric conversion:<\/strong><\/p>\n

                              \n
                            • Identify the number of places to move the decimal point.<\/li>\n<\/ul>\n

                              – Convert a smaller<\/em><\/strong> unit to<\/em><\/strong> a larger<\/em><\/strong> unit: move the decimal point to the left<\/em><\/strong>.<\/p>\n

                              – Convert a larger<\/em><\/strong> unit to<\/em><\/strong> a smaller<\/em><\/strong> unit:\u00a0 move the decimal point to the right<\/em><\/strong>.<\/p>\n

                              \n
                              \n

                              Example 1.3.1<\/p>\n<\/header>\n

                              \n

                              326 mm = (?) m<\/p>\n

                                \n
                              • Identify mm (millimeters<\/em>) and m (meters<\/em>) on the conversion table.<\/li>\n<\/ul>\n

                                Count places from mm to m:\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3 places left<\/p>\n

                                \"\"<\/div>\n
                                  \n
                                • Move 3 decimal places. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(1 m = 1000 mm)<\/li>\n<\/ul>\n

                                  Convert a smaller unit (mm) to a larger (m) unit: move the decimal point to the left.<\/p>\n\n\n\n
                                  326. mm = 0.326 m<\/td>\nMove the decimal point three places to the left (326 = 326.<\/strong>).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

                                   <\/p>\n

                                  \n
                                  \n

                                  Example 1.3.2<\/p>\n<\/header>\n

                                  \n

                                  4.675 hg = (?) g<\/p>\n

                                    \n
                                  • Identify hg (hectograms<\/em>) and g (grams<\/em>) on the conversion table.<\/li>\n<\/ul>\n

                                    Count places from hg to g:\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 2 places right<\/p>\n

                                    \"\"<\/div>\n
                                      \n
                                    • Move 2 decimal places. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(1 hg = 100 g)<\/li>\n<\/ul>\n

                                      Convert a larger unit (hg) to a smaller (g) unit:\u00a0 move the decimal point to the right.<\/p>\n\n\n\n
                                      4.765 hg = 476.5 g<\/td>\nMove the decimal point two places to the right.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
                                      \n

                                      <\/h1>\n

                                      The Unit Factor Method<\/strong><\/h1>\n<\/div>\n

                                      Convert units using the unit factor method (or the factor-label method)\u00a0<\/strong><\/p>\n

                                        \n
                                      • Write the original term as a fraction (over 1).<\/li>\n<\/ul>\n
                                        Example:\u00a0 10g can be written as \"\frac{10g}{1}\"<\/div>\n
                                          \n
                                        • Write the conversion formula as a fraction \"\frac{1}{(\;)}\" or \"\frac{(\;)}{1}\".<\/li>\n<\/ul>\n
                                          Example:\u00a0 1m = 100 cm can be written as \"\frac{1m}{(100cm)}\" or \"\frac{(100cm)}{1m}\"<\/div>\n
                                            \n
                                          • Put the desired or unknown unit on the top.<\/li>\n
                                          • Multiply the original term by \"\frac{1}{(\;)}\" or \"\frac{(\;)}{1}\". (Cancel out the same units).<\/li>\n<\/ul>\n

                                             <\/p>\n

                                            \n
                                            \n

                                            Example 1.3.3<\/p>\n<\/header>\n

                                            \n

                                            1200 g = (?) kg<\/p>\n

                                              \n
                                            • Write the original term (the left side) as a fraction: \"1200 g = \frac{1200 g}{1}\"<\/li>\n
                                            • Write the conversion formula as a fraction. 1 kg = 1000 g: \"\frac{1 kg}{(1000 g)}\"<\/li>\n
                                            • \u201ckg\u201d is the desired unit.<\/li>\n<\/ul>\n
                                                \n
                                              • Multiply: \"1200 g = \frac{1200 \bcancel{g}}{1} \cdot \frac{1 kg}{(1000 \bcancel{g})}\"\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 The units \u201cg\u201d cancel out.<\/li>\n<\/ul>\n

                                                \"= \frac{1200 kg}{1000}\"<\/p>\n

                                                \"= 1.2 kg\"<\/p>\n<\/div>\n<\/div>\n

                                                 <\/p>\n

                                                \n
                                                \n

                                                Example 1.3.4<\/p>\n<\/header>\n

                                                \n

                                                30 cm = (?) mm<\/p>\n

                                                  \n
                                                • Write the original term (the left side) as a fraction: \"30 cm = \frac{30 cm}{1}\"<\/li>\n
                                                • Write the conversion formula as a fraction. 1 cm = 10 mm: \"\frac{(10 mm)}{1cm}\"<\/li>\n<\/ul>\n

                                                  \u201cmm\u201d is the desired unit.<\/p>\n

                                                    \n
                                                  • Multiply: \"30 cm = \frac{30 \bcancel{cm}}{(1 mm)} \cdot \frac{(10 mm)}{1 \bcancel{cm}}\"\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0The units \u201ccm\u201d cancel out.<\/li>\n<\/ul>\n

                                                    \"= \frac{(30)(10) mm}{1}\"<\/p>\n

                                                    \"= 300 mm\"<\/p>\n<\/div>\n<\/div>\n

                                                     <\/p>\n

                                                    Adding and subtracting SI measurements:<\/strong><\/p>\n

                                                    \n
                                                    \n

                                                    Example 1.3.5<\/p>\n<\/header>\n

                                                    \n

                                                    Combine after converting to the same unit.<\/p>\n\n\n\n\n\n
                                                    3 m<\/td>\n<\/td>\n3000 mm<\/td>\n1 m = 1,000 mm<\/td>\n<\/tr>\n
                                                    \u2013\u00a0 \u00a02000 mm<\/span><\/td>\n——–><\/td>\n\u2013\u00a0 \u00a02000 mm<\/span><\/td>\n<\/td>\n<\/tr>\n
                                                    <\/td>\n<\/td>\n1000 mm<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
                                                    25 kg<\/td>\n<\/td>\n25000 g<\/td>\n1 kg = 1000 g<\/td>\n<\/tr>\n
                                                    +\u00a0 \u00a0 \u00a04 g<\/span><\/td>\n——–><\/td>\n+\u00a0 \u00a0 \u00a0 4 g<\/span><\/td>\n<\/td>\n<\/tr>\n
                                                    <\/td>\n<\/td>\n25004 g<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

                                                     <\/p>\n

                                                    \n

                                                    The Relationship between mL<\/em>, g<\/em> and cm3<\/sup><\/strong><\/h1>\n<\/div>\n

                                                    How are mL, g, and cm3<\/sup> related?<\/strong><\/p>\n

                                                    \"\"<\/p>\n

                                                      \n
                                                    • A cube takes up 1 cm3<\/sup> of space (1 cm \u00d7 1 cm \u00d7 1 cm = 1cm3<\/sup>).<\/li>\n
                                                    • A cube holds 1 mL of water and has a mass of 1 gram at 4\u00b0C.<\/li>\n
                                                    • 1 cm3<\/sup> = 1 mL = 1 g<\/li>\n<\/ul>\n

                                                       <\/p>\n

                                                      \n
                                                      \n

                                                      Example 1.3.6<\/p>\n<\/header>\n

                                                      \n

                                                      Convert.<\/p>\n\n\n\n\n
                                                      1) <\/strong>16cm3<\/sup> = ( ? ) g<\/td>\n<\/td>\n<\/tr>\n
                                                      16cm3<\/sup> = 16 g<\/td>\n1 cm3<\/sup> = 1 g<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
                                                      2) <\/strong>9 L = ( ? ) cm3<\/sup><\/td>\n<\/td>\n<\/tr>\n
                                                      9 L = 9000 mL<\/td>\n1 L = 1,000 mL<\/td>\n<\/tr>\n
                                                      = 9000 cm3<\/sup><\/td>\n1 mL = 1 cm3<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
                                                      3) <\/strong>35 cm3<\/sup> = (?) cL<\/td>\n<\/td>\n<\/tr>\n
                                                      35cm3<\/sup> = 35 mL<\/td>\n1 cm3<\/sup> = 1 mL<\/td>\n<\/tr>\n
                                                      = 3.5 cL<\/td>\nmove 1 decimal place left.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n
                                                      4) <\/strong>450 kg = (?) L<\/td>\n<\/td>\n<\/tr>\n
                                                      450 kg = 450,000 g<\/td>\n1 kg = 1,000 g<\/td>\n<\/tr>\n
                                                      = 450,000 mL<\/td>\n1 g = 1 mL<\/td>\n<\/tr>\n
                                                      = 450 L<\/td>\n1 L = 1,000 mL<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

                                                       <\/p>\n

                                                      \n
                                                      \n

                                                      Example 1.3.7<\/p>\n<\/header>\n

                                                      \n

                                                      A swimming pool measures 10 m by 8 m by 2 m. How many kilolitres<\/em><\/strong> of water will it hold?<\/p>\n\n\n\n\n\n\n\n
                                                      V<\/em> = w<\/em> l h <\/em>= (8m) (10m) (2m) = 160 m3<\/sup><\/td>\n160 m3<\/sup> = ( ? ) kL<\/td>\n<\/tr>\n
                                                      160m3<\/sup> = 160,000,000 cm3<\/sup><\/td>\n1 m = 100 cm, 3<\/strong> \u00d7 2 = 6, move 6 places right for volume.<\/td>\n<\/tr>\n
                                                      160,000,000 cm3<\/sup> = 160,000,000 mL<\/td>\n1 mL = 1 cm3<\/sup><\/td>\n<\/tr>\n
                                                      160,000,000 mL = 160 kL<\/td>\n1 kL = 1,000,000 mL<\/td>\n<\/tr>\n
                                                      160 m3<\/sup> = 160 kL<\/td>\nThe swimming pool will hold 160 kL of water.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
                                                      \n

                                                       <\/p>\n

                                                      Practice questions<\/strong><\/h1>\n

                                                      1.<\/strong> Convert each of the following measurements<\/span>:<\/p>\n<\/div>\n

                                                      a. <\/strong>439 mm = ( ? ) m<\/p>\n

                                                      b. <\/strong>48.3 mL = ( ? ) kL<\/p>\n

                                                      c. <\/strong>7230 g = ( ? ) kg<\/p>\n

                                                      d. <\/strong>52 cm = ( ? ) mm<\/p>\n

                                                      3.<\/strong> Combine:<\/p>\n

                                                      a. <\/strong>7 m \u2013 3000 mm = ( ? ) mm<\/p>\n

                                                      b. <\/strong>63 kg + 6 g = ( ? ) g<\/p>\n

                                                      4.<\/strong> Complete:<\/span><\/p>\n

                                                      a. <\/strong>38 cm3<\/sup> = (\u00a0 \u00a0 \u00a0 \u00a0) g<\/p>\n

                                                      b. <\/strong>5 L = (\u00a0 \u00a0 \u00a0 \u00a0) cm3<\/sup><\/p>\n

                                                      c. <\/strong>18 L of water has a volume of ___________ cm3<\/sup> .<\/p>\n

                                                      d. <\/strong>A water tank measures 45 cm by 35 cm by 25 cm. How many kilolitres of water will it hold?<\/p>\n

                                                       <\/p>\n

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