Metric Units of Length

10A Metric units of length CONSOLIDATING LEARNING INTENTIONS • To be able to choose a suitable unit for a length within the metric system • To be able to convert between metric lengths (km, m, cm and mm) • To be able to read a length shown on a ruler or tape measure The metric system was developed in France in the 1790s and is the universally accepted system today. The word metric comes from the Greek word metron, meaning ‘measure’. It is a decimal system where length measures are based on the unit called the metre. The definition of the metre has changed over time. Originally, it was proposed to be the length of a pendulum that beats at a rate of one beat per second. It was later defined as 1/10 000 000 of the distance from the North Pole to the equator on a line on Earth’s surface passing through Paris. In 1960, a metre became 1 650 763.73 wavelengths of the spectrum of the krypton-86 atom in a vacuum. In 1983, the metre was defined as the distance that light travels in 1/299 792 458 seconds inside a vacuum. To avoid the use of very large and very small numbers, an appropriate unit is often chosen to measure a length or distance. It may also be necessary to convert units of length. For example, 150 pieces of timber, each measured in centimetres, may need to be communicated as a total length using metres. Another example might be that 5 millimetres is to be cut from a length of timber 1.4 metres long because it is too wide to fit a door opening that is 139.5 centimetres wide. A carpenter may need to measure lengths in metres, centimetres and millimetres. Making accurate measurements and converting units are essential skills for construction workers. Lesson starter: How good is your estimate? Without measuring, guess the length of your desk, in centimetres. • • • Now use a ruler to find the actual length in centimetres. Convert your answer to millimetres and metres. If you lined up all the class desks end to end, how many desks would be needed to reach 1 kilometre? Explain how you got your answer. KEY IDEAS ■ Metric system • • • km cm m ÷ 1000 ■ Conversion × 10 × 100 × 1000 1​ centimetre (cm) = 10 millimetres (mm)​ ​1 metre (m) = 100 centimetres (cm)​ ​1 kilometre (km) = 1000 metres (m)​ mm ÷ 10 ÷ 100 • When converting to a smaller unit, multiply by ​10​or ​100​or ​1000​. The decimal point appears to move to the right. For example: 28 cm = (28 × 10) mm 2.3 m = (2.3 × 100) cm ​   ​ ​ ​    ​ ​ ​ ​ ​ = 230 cm ​ = 280 mm • When converting to a larger unit, divide by a power of ​10​(i.e. ​10, 100, 1000​). The decimal point appears to move to the left. For example: 47 mm = (47 ÷ 10) cm 4600 m = (4600 ÷ 1000) km ​ ​ ​ ​    ​    ​ ​ ​ ​ = 4.7 cm ​ = 4.6 km ■ When reading scales, be sure about what units are showing on the scale. This scale shows ​36 mm​. mm cm 1 2 3 4 BUILDING UNDERSTANDING 1 Use the metric system to state how many: a millimetres in ​1​ centimetre b centimetres in ​1​ metre c metres in ​1​ kilometre d millimetres in ​1​ metre e centimetres in ​1​ kilometre f millimetres in ​1​ kilometre. 2 State the missing number or word in these sentences. a When converting from metres to centimetres, you multiply by _______. b When converting from metres to kilometres, you divide by _______. c When converting from centimetres to metres, you _______ by ​100.​ d When converting from kilometres to metres, you ________ by ​1000​. 3 Calculate each of the following. a ​100 × 10​ c ​100 × 1000​ b 1​ 0 × 100​ d ​10 × 100 × 1000​ 4 a When multiplying by a power of ​10​, in which direction does the decimal point move – left or right? b When dividing by a power of ​10​, in which direction does the decimal point move – left or right?