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Length 1 foot = 12 inches 1 yard =3 feet 1 mile = 1760 yards Converting to metric length 1 inch = 2.5 cm 1 foot = 30.5 cm 1 m = 39 inches 1 mile = 1.6 km or 5 miles = 8 km Converting metric and Imperial Measures in Length Convert 40cm into inches. 1 inch = 2.5 cm 40/2.5 = 16 inches Tim is 6 feet 2 inches tall. Estimate Tims height in cm. 1 foot = 12 inches 6 feet =6 x 12 = 72 inches Total height = 72 + 2 = 74 inches 1 inch = 2.5 cm 74 x 2.5 = 185 cm Conversions on length How far is 32 km in miles? 1 mile = 1.6 km 32/1.6 = 20 miles Mass 1 pound = 16 ounces 14 pounds = 1 stone 240 pounds = 1 ton Converting to metric length 1 kg = 2.2 pounds Converting Imperial to Metric Mass Change 5 kg to pounds. 1 kg = 2.2 pounds 5 kg = 5 x 2.2 = 11 pounds James weighs 10 stones 6 pounds. Estimate his weight in kilograms. 1 stone = 14 pounds 10 stones = 10 x 14 = 140 pounds Total weight in pounds = 140 + 6 = 146 pounds 1 kg = 2.2 pounds 146 pounds/2.2 = 66 kg Capacity and Volume 1 gallon = 8 pints Converting to metric units 1 litre = 1.75 pints 1 litre = 0.2 gallons Conversions on mass How many pints are there in a 4 litre carton of milk? 1 litre = 1.75 pints 4 x 1.75 = 7 pints The capacity of a cars petrol tank is 12 gallons. How much does the petrol tank hold in litres? 1 litre = 0.2 gallons 12/0.2 = 60 litres Discrete and Continuous Measures Discrete Measures Can only take particular measures The number of people on the bus is 42. My shoe size is 4 ½. Continuous Measures Measures that can lie within a range of possible values Height of a mountain Weight Age Continuous Measures Examples Jane is 160 cm tall to the nearest 10 cm. What are the limits between which her true height lies? The smallest value is 155 cm The highest value is 164.99999999999 cm which we take as 165 cm 155cm≤ Janes height<165 cm Continuous Measures Examples Jane is 160 cm tall to the nearest 1 cm. What are the limits between which her true height lies? The smallest value is 159.5 cm The highest value is 160.4999999999 cm We take it as 160.5 cm. 159.5 cm≤ Janes height < 160.5 cm Dimensions and Formulae Length (L) has a dimension of 1. Area has dimension of Length x Length (L²) 2-D Volume has dimension of Length x Length x Length (L³) 3-D Dimensions and Formulae examples 1) 2) 3) 4) In each of these expressions the letters a, b, and c represent lengths. Use dimensions to check whether the expressions could represent perimeter, area or volume. 2a + 3b + 4c 2a²b +abc 3a² +2b(a+c) 3a + 2ab + c³