Mathematics and Units of Measurement 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120 7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160 9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220 12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 MULTIPLICATION CHART NUMBER NOTATION The decimal number system uses base 10. Place value: 123,456,789.012 MILLIONS THOUSANDS ONES Each section shows hundreds, tens, and ones. Expanded notation: 6,824 = 6 x 103 + 8 x 102 + 2 x 101 + 4 x 100 Scientific notation: 6,800 = 6.8 x 103 Symbols ORDER OF OPERATIONS P Do operations within parentheses ( ) and other grouping symbols. E Do exponents 2 and roots . MD Do multiplication x and division ÷ in order from left to right. AS Do addition + and subtraction – in order from left to right. FRACTIONS, DECIMALS, PERCENTAGES 3 – numerator _ 5 – denominator To add or subtract fractions, first obtain a common denominator: 1 2 5 6 11 --- + --- = --- + --- = -- 3 5 15 15 15 To multiply: 1 2 1 x 2 2 --- x --- = --------- = --- 3 5 3 x 5 15 To divide, multiply the first fraction by the reciprocal of the second fraction: 2 1 2 6 12 =4 --- ÷ --- = --- x --- = ---- 3 6 3 1 3 1 = 1.0 = 100% 3/4 = 0.75 = 75% 2/3 = 0.6– = 66.6– % 1/2 = 0.5 = 50% 1/3 = 0.3– = 33.3– % 1/4 = 0.25 = 25% 1/5 = 0.2 = 20% 1/6 = 0.16– = 16.6– % 1/8 = 0.125 = 12.5% 1/9 = 0.1– = 11.1– % 1/10 = 0.1 = 10% 1/12 = 0.083– = 8.3– % COMMON UNITS used with the International System Length 1 millimetre (mm) = 0.04 inches (in.) 1 metre (m) = 39.4 inches = 3.3 feet (ft.) = 1.1 yards (yd.) 1 kilometre (km) = 1093.6 yards (yd.) = 0.6 miles (mi.) Capacity 1 tablespoon (Tbsp.) = 3 teaspoons (tsp.) 1 cup (c.) = 8 fl. oz. = 236.59 mL 1 pint (pt.) = 2 c. = 473.18 mL 1 quart (qt.) = 2 pt. = 4 c. = 32 fl. oz. = 946.35 mL 1 gallon (gal.) = 3.7854 L Area 1 ft.2 = 144 in.2 1 yd.2 = 9 ft.2 1 acre = 4 840 yd.2 1 m2 = 10,000 cm2 1 hectare (ha) = 10,000 m2 1 km2 = 100 ha Mass 1 pound (lb.) = 16 ounces (oz.) 1 ton, UK (tn.) = 2,240 lbs. 1 kg = 1,000 g 1 tonne (t) = 1,000 kg Length/Area to go from to multiply by cm → in. 0.39 in. → cm 2.54 m → ft. 3.28 ft. → m 0.30 km → mi. 0.62 mi. → km 1.61 m2 → ft.2 10.76 ft.2 → m2 0.09 km2 → mi.2 0.39 mi.2 → km2 2.59 Weight/Capacity to go from to multiply by g → oz. 0.0353 oz. → g 28.35 kg → lbs. 2.2046 lbs. → kg 0.4536 t → tn. 0.9842 tn. → t 1.0161 mL → fl. oz. 0.0338 fl. oz. → mL 29.574 L → US gal. 0.2642 US gal. → L 3.785 TEMPERATURE °C = 5/9 (°F - 32) °F = 9/5 °C + 32 SQUARES AND SQUARE ROOTS Is less than Is greater than Is equal to Is approximate to Is less than or equal to Is greater than or equal to n 1 2 3 4 5 6 7 8 9 10 12 15 20 25 100 1/2 1/4 n2 1 4 9 16 25 36 49 64 81 100 144 225 400 625 10,000 1/4 1/16 n 1 1.414 1.732 2 2.236 2.449 2.646 2.828 3 3.162 3.464 3.873 4.472 5 10 0.707 1/2 MEASUREMENTS AND CONVERSIONS 1,000 100 10 1 .1 .01 .001 KILO HECTO DECA DECI CENTI MILLI km hm dam m dm cm mm kg hg dag g dg cg mg kL hL daL L dL cL mL TENTHS HUNDREDTHS THOUSANDTHS MEASUREMENT.........ABBREV.....RELATION metre.. . . . . . . . . . . . m.. . . length hectare.. . . . . . . . . . ha.. . . area kelvin.. . . . . . . . . . . . . K. . . . thermodynamic temp. kilogram. . . . . . . . . kg.. . . mass litre. . . . . . . . . . . . . . . . L. . . . volume or capacity second. . . . . . . . . . . . s.. . . . time hertz.. . . . . . . . . . . . . Hz.. . . frequency degree Celsius.. . ˚C.. . . temperature joule.. . . . . . . . . . . . . . J.. . . . energy, work pascal. . . . . . . . . . . . Pa.. . . pressure, stress newton.. . . . . . . . . . N. . . . force watt. . . . . . . . . . . . . . W.. . . power, radiant flux ampere.. . . . . . . . . . .A. . . . electric current volt. . . . . . . . . . . . . . . . V. . . . electric potential RESOURCE PAGES R–9
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