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, such as absolute value and square root. 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 = 0.1 –6 = 16. –6% 1/8 = 0.125 = 12.5% 1/9 = 0.1– = 11.1– % 1/10 = 0.1 = 10% 1/12 = 0.08 –3 = 8. –3% Is less than Is greater than Is equal to Is approximate to Is less than or equal to Is greater than or equal to SQUARES AND SQUARE ROOTS 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 Length 1 millimetre (mm) = 0.04 inches (in.) 1 metre (m) = 39.4 inches (in.) = 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.) = 14.787 mL 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 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 Mathematics and Units of Measurement COMMON UNITS used with the International System 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 TEMPERATURE °C = 5/9 (°F – 32) °F = 9/5 °C + 32 TENTHS HUNDREDTHS THOUSANDTHS R–9 RESOURCE PAGES
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