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Step-by-step practice: Maths · Level 5Chapter 8 · Metric length, mass and capacity
Step-by-step Maths Level 5 · Metric length, mass and capacity · Lesson 8.1

Step-by-step Maths Level 5: Converting length: km, m, cm and mm

Part of the Step-by-step Maths Level 5 metric length, mass and capacity chapter. Chapter overview · whole chapter on one page

8.1

Converting length: km, m, cm and mm

Level 5
Convert between km and m, m and cm, and cm and mm

1 km = 1,000 m, 1 m = 100 cm, and 1 cm = 10 mm. Going to a smaller unit makes the number bigger, so multiply.

To change a number of centimetres into metres and centimetres, divide by 100. 340 cm = 3 m 40 cm.

Key ideas

  • 1 km = 1,000 m; 1 m = 100 cm; 1 cm = 10 mm.
  • Smaller unit: multiply. Bigger unit: divide.
  • Write both parts with their units.
Worked example 8.1.1
Change 3 km to metres.

Method. Multiply by 1,000 to change kilometres into metres.

  1. Use the rule. 1 kilometre is 1,000 metres.
    1 km = 1,000 m
  2. Multiply the kilometres by 1,000. Each kilometre is 1,000 metres.
    3 × 1,000 = 3,000
  3. Write the answer with the unit. The unit is metres.
    3,000 m

Check. Check: 3,000 ÷ 1,000 = 3.

Watch out. Going to a smaller unit makes the number bigger. Multiply.

Worked example 8.1.2
Change 4 m to cm.

Method. Multiply by 100 to change m into cm.

  1. Use the rule. 1 m is 100 cm.
    1 m = 100 cm
  2. Multiply the m by 100. Each m has 100 cm.
    4 × 100 = 400
  3. Write the answer with the unit. The unit is cm.
    400 cm

Check. Check: 400 ÷ 100 = 4.

Watch out. A smaller unit gives a bigger number. Multiply by 100.

Worked example 8.1.3
Change 340 cm to m and cm.

Method. Divide by 100 to find the whole m; the remainder is the cm.

  1. Use the rule. 1 m is 100 cm.
    1 m = 100 cm
  2. Share 340 cm into groups of 100. Each group is one m.
    340 ÷ 100 = 3 r 40
  3. Write the answer. 3 whole m and the cm left over.
    3 m 40 cm

Check. Check: 3 × 100 + 40 = 340.

Watch out. Use a space between the two parts, and the unit after each: 3 m 40 cm.

Watch out

Watch out. 1 m is 100 cm, not 10 cm. Check the number of zeros for each unit.

Exam tip

Grown-up tip. Use a metre stick or a ruler. Ask: “How many centimetres in one metre? How many millimetres in one centimetre?”

Exercise 8A  Practice: converting length

Non-calculator
1
FChange 1,888 cm to m and cm.
2
FChange 32 mm to cm and mm.
3
FChange 1,253 cm to m and cm.
4
FChange 14 km to metres.
5
FChange 2 km to metres.
6
FChange 8 m to cm.
7
FChange 9 m to cm.
8
FChange 981 cm to m and cm.
9
FChange 5 cm to mm.
10
FChange 4 cm to mm.
11
FChange 1,127 cm to m and cm.
12
FChange 8 cm to mm.
13
FChange 1,086 cm to m and cm.
14
FChange 111 mm to cm and mm.
15
FChange 17 m to cm.
16
FChange 3 km to metres.

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