Converting Between Units

Mathematics · Ratio & Proportion · ages 11-12

Name ______________________ Date ____________

2.5 hours is the same as 150 minutes. True or false?
Circle one: True False
How many square centimetres are in 1 square metre?
- 100,000
- 10,000
- 1,000
True or false: to convert hours into seconds, you multiply by 60 only once.
Circle one: True False
How many cubic centimetres equal 1 litre?
- 10
- 100
- 1000
Why does m² to cm² multiply by 10,000 and not 100?
- 1 m² is a 100-by-100 square of cm²
- Metres are 1000 cm
- Area and length convert the same
- You always add four zeros
How many cm³ are in 3 litres?
Answer: ______________
Convert 3 m² into cm².
Answer: ______________
Convert 1750 cm³ into litres.
Answer: ______________
Priya converts 5 m² to cm² by multiplying by 100, getting 500 cm². What did she do wrong?
- She should multiply by 100² = 10,000, not 100
- She should divide by 100 instead of multiplying
- She should use 1000 as the conversion factor
A tap fills a bucket at 500 cm³ per minute. After 4 minutes, how many litres are in the bucket?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

True · 2 x 60 = 120 plus 0.5 x 60 = 30: 150 minutes.
10,000 · A metre is 100 cm, so 1 m² = 100 × 100 = 10,000 cm². Squaring the scale factor is the key step.
False · You need two steps: hours to minutes (×60), then minutes to seconds (×60 again).
1000 · 1 litre equals 1000 millilitres, and each millilitre is the same as 1 cm³, so 1 litre = 1000 cm³.
1 m² is a 100-by-100 square of cm² · Area squares the linear factor: 100 x 100 = 10,000.
3000 · 1 litre is 1000 cm³, so 3 litres is 3 x 1000 = 3000 cm³.
30000 · 1 m² holds 100 x 100 = 10,000 cm², so 3 m² is 30,000 cm².
1.75 · 1000 cm³ fills a litre, so 1750 / 1000 = 1.75 litres.
She should multiply by 100² = 10,000, not 100 · Area covers two dimensions, so the scale factor must be squared: 100 × 100 = 10,000, giving 50,000 cm².
2 · 500 × 4 = 2000 cm³, and 2000 cm³ ÷ 1000 = 2 litres.