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Metric and imperial conversion drill

Convert inches to millimetres and feet to metres, both ways. Type the answer; it is marked with a small tolerance so a reasonable rounding counts, and the working is shown when you miss.

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Cet exercice a besoin de JavaScript pour générer et corriger les questions. Activez-le pour vous exercer — l’explication ci-dessous fonctionne dans les deux cas.

The two constants

One inch is exactly 25.4 mm; one foot is exactly 0.3048 m. Everything here runs off those two. Inches to millimetres: multiply by 25.4 — so 3.5" is 3.5 × 25.4 = 88.9 mm. Feet to metres: multiply by 0.3048 — so 10 ft is 10 × 0.3048 = 3.048 m. Reverse each by dividing instead. Because both figures are exact definitions, the conversions are exact too; the only rounding is whatever you choose at the end.

Three worked, the way you would do them on a box lid

1. A tape reading to millimetres — 3 5/8"

  1. Turn the fraction into a decimal first: 5 ÷ 8 = 0.625, so 3 5/8" is 3.625".
  2. Inches to millimetres is multiply by 25.4: 3.625 × 25.4.
  3. Split it: 3 × 25.4 = 76.2, and 0.625 × 25.4 = 15.875. Add: 92.075 mm, call it 92 mm.
The quick check

Four inches is just over 100 mm (4 × 25.4 = 101.6). Three and a bit inches should land a bit under that. 92 fits; 920 or 9.2 would not. Always do the size check before you trust the digits.

2. A print dimension to inches — 400 mm

  1. Millimetres to inches is divide by 25.4: 400 ÷ 25.4.
  2. Rough it first: 400 ÷ 25 = 16, so the answer is a touch under 16.
  3. Properly: 400 ÷ 25.4 = 15.75". On the tape that is 15 3/4" — a clean mark, which is a hint you did it right.
Getting from 15.75 to a tape fraction

The decimal part is 0.75. Multiply by 16: 0.75 × 16 = 12 sixteenths, which reduces to 3/4. If the sixteenths had come out as, say, 11.8, you would round to 12/16 = 3/4 and know the mark was between graduations. The fraction / decimal drill is that step on its own.

3. Feet and inches to metres — 12' 6"

  1. Get it into one unit first. 6" is half a foot, so 12' 6" is 12.5 ft.
  2. Feet to metres is multiply by 0.3048: 12.5 × 0.3048.
  3. 12 × 0.3048 = 3.6576 and 0.5 × 0.3048 = 0.1524. Add: 3.81 m.
The mental version

A metre is about 3.28 ft, so 12.5 ÷ 3.28 ≈ 3.8. Or: 10 ft is about 3 m, and the other 2.5 ft is about 0.76 m. Either rough road gets you close enough to know whether the exact answer is sensible.

The slips

  • Divided when you should multiplyMillimetre numbers are always bigger than the inch numbers they came from, and metre numbers always smaller than feet. If the answer went the wrong way in size, you used the wrong operation.
  • Mixed the two constants25.4 is inches to millimetres. 0.3048 is feet to metres. Feet times 25.4 is nothing at all. Say the units out loud before you press the button.
  • Left the inches in the feet12' 6" is 12.5 ft, not 12.6. Convert the inches to a fraction of a foot (divide by 12) before you touch the constant.
Try one before the drill: 7 1/4" in millimetres, and 2.4 m in feet

7 1/4" = 7.25". 7.25 × 25.4 = 184.15 mm, so 184 mm. Size check: seven inches is a bit under 180, and this is a bit over — right neighbourhood. Then 2.4 ÷ 0.3048 = 7.87 ft. Size check: a metre is a bit over three feet, so 2.4 m is a bit under eight. Both pass.

Questions fréquentes

How many millimetres are in an inch?

Exactly 25.4. It is a defined value, not a rounded one, so an inch is 25.4 mm on the nose. To go from inches to millimetres multiply by 25.4; to go back, divide by 25.4.

And feet to metres?

A foot is exactly 0.3048 metres. Multiply feet by 0.3048 for metres, divide metres by 0.3048 for feet. Both conversions are exact definitions, which is why they never drift.

Why practise conversions?

Because prints, fittings and materials mix the two systems, and doing the swap in your head keeps you moving instead of reaching for a phone. A little drilling makes 25.4 and 0.3048 as automatic as your times tables.

Voir aussi

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