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Math · Measurement & Reasoning
Metric Length: Estimate, Convert and Keep the Units
Learn how millimetres, centimetres, metres and kilometres relate, choose a sensible unit, and defend comparisons rather than guessing from the digits alone.
The idea
Every measurement needs both a number and a unit. 'The ribbon is 35' is incomplete. 'The ribbon is 35 centimetres long' lets another person understand and check the claim.
Metric length units connect in groups of ten, one hundred and one thousand: 10 millimetres = 1 centimetre, 100 centimetres = 1 metre, and 1,000 metres = 1 kilometre.
Converting a unit does not change the actual object. A 200-centimetre rope and a 2-metre rope can be exactly the same length.
A rain gauge reports depth in millimetres. That is a length measurement; the litres of water collected would also depend on the area receiving rain. Do not switch millimetres and millilitres just because the names look alike.
Worked examples
Example 1 · Pick a sensible unit
Should a pencil's length be reported as 16 centimetres, 16 metres, or 16 kilometres?
- Picture a normal pencil against a ruler.
- A centimetre is a small unit suitable for hand-held objects.
- Metres and kilometres are much too large for the intended measurement.
16 centimetres is sensible.
Example 2 · Convert centimetres to metres
A jump rope is 245 centimetres long. Express it in metres and centimetres.
- 100 centimetres = 1 metre.
- 245 centimetres = 200 centimetres + 45 centimetres.
- 200 centimetres = 2 metres.
2 metres 45 centimetres (2.45 m).
Example 3 · Convert millimetres to centimetres
A rain gauge shows 28 millimetres. Express the same depth in centimetres and millimetres.
- 10 millimetres = 1 centimetre.
- 28 millimetres = 20 millimetres + 8 millimetres.
- 20 millimetres = 2 centimetres.
2 centimetres 8 millimetres (2.8 cm).
Example 4 · Compare in one unit
One ribbon is 1 metre 35 centimetres. Another is 142 centimetres. Which is longer, and by how much?
- Change 1 metre 35 centimetres to 135 centimetres.
- Compare 135 centimetres with 142 centimetres.
- 142 − 135 = 7 centimetres.
The 142 cm ribbon is 7 cm longer.
Example 5 · Reason with kilometres
A family walks 2 kilometres 300 metres in the morning and 1 kilometre 750 metres later. What is the total distance?
- Convert: 2 km 300 m = 2,300 m; 1 km 750 m = 1,750 m.
- Add 2,300 + 1,750 = 4,050 metres.
- 4,050 metres = 4 kilometres 50 metres.
- Estimate: a little over 4 km makes sense.
4 km 50 m.
Common mistakes
These are tempting because they use familiar operations. Check what the question is actually measuring.
Why this fails: First convert to the same unit: 1.2 m = 120 cm; 135 cm is longer.
Why this fails: For the same object, changing centimetres to metres produces fewer units: 200 cm = 2 m.
Why this fails: 3 km = 3,000 m, so add 80 m to get 3,080 m.
Why this fails: Millimetres describe depth; millilitres describe capacity or volume.
Why this fails: Say 'about 40 cm' for an estimate; use an instrument if precision matters.
Foundation
Foundation practice
Name sensible units and read basic conversions.
1. Which unit best describes the thickness of a coin: millimetres, metres or kilometres?
2. Which unit is practical for the distance between two nearby towns?
3. How many centimetres are in 1 metre?
4. How many millimetres are in 3 centimetres?
5. How many metres are in 2 kilometres?
6. Does a ribbon grow when we write its length as 150 cm instead of 1.5 m?
Convert with precision
Convert with precision practice
Keep every quantity equivalent.
7. Convert 375 cm to metres and centimetres.
8. Convert 42 mm to centimetres and millimetres.
9. Convert 5 km 60 m to metres.
10. Convert 2 m 8 cm to centimetres.
11. Which is longer: 185 cm or 1 m 95 cm?
12. Which is smaller: 75 mm or 8 cm?
Solve in context
Solve in context practice
Explain the operation and the unit.
13. A garden path is 4 m. A child walks 125 cm, then 175 cm. How far remains?
14. A plant is 78 cm tall and grows 15 cm. How far from 1 metre is it?
15. A route measures 1 km 250 m plus 850 m. Find its length.
16. A rain gauge reads 18 mm on Monday and 11 mm on Tuesday. How much greater is Monday's depth?
17. Two playgrounds are 750 m apart. Is this less than or more than 1 km? By how much?
18. A door is described as 210 km tall. What likely went wrong?
Transfer and justify
Transfer and justify practice
Decide what the data do and do not prove.
19. A student guesses a desk is 1 m long. What would make that claim more precise?
20. Why are 0.5 m and 50 cm equivalent?
21. A friend says '30 mm of rain means exactly 30 mL of water in every bucket.' What is the error?
22. A 3-metre ribbon is cut into two pieces of 85 cm and 115 cm. How much remains?
23. A school map labels a route as 1.3 km. Express it in metres and explain what happens to the number.
24. An estimate says a hallway is 20 m long; a measuring wheel gives 18 m 40 cm. How far off was the estimate?
25. A wooden strip is 14 cm long. Add a piece that is 86 mm long. What total length is that in millimetres?
26. Two days have a total of 18 mm of rain. Does this prove each day received 9 mm?
Answer key
- 1. millimetres
A coin is only a few millimetres thick. - 2. kilometres
A town-to-town trip covers much more than a few metres. - 3. 100 centimetres
100 cm = 1 m. - 4. 30 millimetres
3 × 10 mm = 30 mm. - 5. 2,000 metres
2 × 1,000 m = 2,000 m. - 6. No
A change of unit does not change physical length. - 7. 3 m 75 cm
375 cm = 300 cm + 75 cm. - 8. 4 cm 2 mm
40 mm = 4 cm, leaving 2 mm. - 9. 5,060 m
5,000 + 60 = 5,060 m. - 10. 208 cm
200 cm + 8 cm = 208 cm. - 11. 1 m 95 cm, by 10 cm
1 m 95 cm = 195 cm; 195 − 185 = 10 cm. - 12. 75 mm, by 5 mm
8 cm = 80 mm; 75 mm is smaller. - 13. 1 m
125 + 175 = 300 cm; 400 − 300 = 100 cm = 1 m. - 14. 7 cm shorter than 1 m
78 + 15 = 93 cm; 100 − 93 = 7 cm. - 15. 2 km 100 m
1,250 + 850 = 2,100 m. - 16. 7 mm
18 − 11 = 7 mm; both figures measure depth. - 17. 250 m less than 1 km
1 km = 1,000 m; 1,000 − 750 = 250 m. - 18. The unit is unreasonable; 210 cm (2.10 m) is plausible.
Length units must fit real-world scale. - 19. Measure it with a metre stick or tape measure and report the unit.
An estimate should not be described as an exact reading. - 20. 1 m = 100 cm, so half a metre is 50 cm.
Changing units keeps the same physical distance. - 21. Millimetres measure rainfall depth; collected volume depends on the opening area.
Capacity and length are different quantities. - 22. 100 cm or 1 m
300 − 85 − 115 = 100 cm. - 23. 1,300 m; smaller units mean more units for the same length.
1.3 × 1,000 = 1,300. - 24. 1 m 60 cm
20 m − 18.4 m = 1.6 m = 1 m 60 cm. - 25. 226 mm
14 cm = 140 mm, then 140 + 86 = 226 mm. - 26. No. The two readings could differ and still add to 18 mm.
A total does not show how the amount was distributed across days.