Topics › KS3 › Ratio & proportion
Unit conversions
-
Convert $3.5$ m to centimetres.
A
Option A:
350 cm
B
Option B:
35 cm
C
Option C:
3500 cm
D
Option D:
3.50 cm
Answer and misconceptions
A
Option A:
350 cm
✓ Correct
B
Option B:
35 cm
✗
Thinks 1 m = 10 cmMultiplies by 10 instead of 100.
C
Option C:
3500 cm
✗
Thinks 1 m = 1000 cmConfuses centimetres with millimetres and multiplies by 1000.
D
Option D:
3.50 cm
✗
Adds a zero instead of multiplyingThinks multiplying means writing a zero on the end, which does not change a decimal.
-
Convert 2500 g to kilograms.
A
Option A:
25 kg
B
Option B:
$2\,500\,000$ kg
C
Option C:
2.5 kg
D
Option D:
250 kg
Answer and misconceptions
A
Option A:
25 kg
✗
Thinks 1 kg = 100 gDivides by 100 instead of 1000.
B
Option B:
$2\,500\,000$ kg
✗
Multiplies when changing to a larger unitKilograms are bigger than grams, so there should be fewer of them: divide, do not multiply.
C
Option C:
2.5 kg
✓ Correct
D
Option D:
250 kg
✗
Thinks 1 kg = 10 gDivides by 10 instead of 1000.
-
Write $2.5$ hours in hours and minutes.
A
Option A:
2 h 50 min
B
Option B:
2 h 30 min
C
Option C:
2 h 5 min
D
Option D:
4 h 10 min
Answer and misconceptions
A
Option A:
2 h 50 min
✗
Reads the decimal part as minutesTreats 0.5 h as 50 minutes, as if there were 100 minutes in an hour.
B
Option B:
2 h 30 min
✓ Correct
C
Option C:
2 h 5 min
✗
Reads .5 as 5 minutesTakes the digit after the point as the number of minutes.
D
Option D:
4 h 10 min
✗
Multiplies by 100 to get minutesDoes 2.5 × 100 = 250 minutes, which is 4 h 10 min; there are 60 minutes in an hour, so 2.5 h = 150 min.
-
How many cm² are there in 1 m²?
A
Option A:
100
B
Option B:
200
C
Option C:
1000
D
Option D:
$10\,000$
Answer and misconceptions
A
Option A:
100
✗
Uses the length conversion for area1 m = 100 cm, but a square metre is 100 cm by 100 cm, so 100 × 100.
B
Option B:
200
✗
Doubles the length factor for square unitsThinks squared means ×2, so 100 × 2 = 200.
C
Option C:
1000
✗
Confuses centimetres with millimetresRemembers 1 m = 1000 mm and uses that number.
D
Option D:
$10\,000$
✓ Correct
-
Convert 6 cm³ to mm³.
A
Option A:
6000 mm³
B
Option B:
60 mm³
C
Option C:
600 mm³
D
Option D:
18 mm³
Answer and misconceptions
A
Option A:
6000 mm³
✓ Correct
B
Option B:
60 mm³
✗
Uses the length factor for volume1 cm = 10 mm, but 1 cm³ = 10 × 10 × 10 = 1000 mm³.
C
Option C:
600 mm³
✗
Uses the area factor for volumeMultiplies by 10 × 10 = 100, which is the factor for cm² to mm².
D
Option D:
18 mm³
✗
Thinks cubed means multiply by 3Reads the ³ as ×3 and works out 6 × 3.