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Fraction and decimal drill

Convert between fractions of an inch and their decimals, both directions, to the nearest sixteenth. Pick the answer and keep your streak alive.

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This drill needs JavaScript to generate and mark questions. Turn it on to practice — the explanation below works either way.

The method, both ways

Fraction to decimal: divide the top by the bottom. 5/16 = 5 ÷ 16 = 0.3125. Decimal to fraction: multiply by sixteen and reduce. 0.75 × 16 = 12, so 12/16, which reduces to 3/4. The whole of it is division one way and multiplication the other, plus the habit of reducing the fraction to its simplest form.

Three worked

1. Fraction to decimal — 7/16

  1. Top divided by bottom: 7 ÷ 16.
  2. 16 goes into 7 zero times; into 70 four times (64), remainder 6; into 60 three times (48), remainder 12; into 120 seven times (112), remainder 8; into 80 five times exactly.
  3. 0.4375. Every sixteenth ends in 25 or 75, which is a quick way to spot a slip.
The shortcut nobody tells you

One sixteenth is 0.0625. So any number of sixteenths is that many times 0.0625: 7 × 0.0625 = 0.4375. Learn one number and you have the whole tape. Eighths are 0.125 each, quarters 0.25.

2. Decimal to fraction — 0.8125

  1. Multiply by 16 to get sixteenths: 0.8125 × 16 = 13.
  2. A whole number, so it sits exactly on a mark: 13/16.
  3. Can it reduce? 13 is prime, so no. 13/16".
When it does not come out whole

0.79 × 16 = 12.64 — between the 12th and 13th marks, nearer the 13th. Round to 13/16 and know you are about a sixty-fourth off. If the job needs better than a sixteenth, the tape is the wrong tool anyway.

3. A mixed number — 2 3/8" as a decimal, and back

  1. Leave the 2 alone. 3 ÷ 8 = 0.375. So 2 3/8" = 2.375".
  2. Back the other way: the whole part is 2; 0.375 × 16 = 6, so 6/16.
  3. Reduce: 6 and 16 both divide by 2 → 3/8. 2 3/8". Round trip clean.
Why reduce at all

Because the tape is labelled in the reduced form. Nobody says "six sixteenths"; the mark you are looking for is the 3/8 line, which is longer than the sixteenth lines around it. Reducing is how you find the right length of line to look for.

The slips

  • Divided the wrong way3/8 is 3 ÷ 8, always top by bottom. 8 ÷ 3 = 2.67 is a giveaway — a fraction of an inch is never bigger than one.
  • Forgot to reduce10/16 is not wrong, but the tape says 5/8. Halve both until one of them is odd.
  • Used 10 instead of 160.5 × 10 is 5, so "5/10"? No. The tape is in sixteenths; multiply the decimal by 16.
Try one before the drill: 11/16 as a decimal, and 0.5625 as a fraction

11 × 0.0625 = 0.6875. Then 0.5625 × 16 = 9, so 9/16 — 9 is odd, so it does not reduce. Both land exactly on a mark, which is what a sixteenth should do.

Questions people ask

How do I turn a fraction of an inch into a decimal?

Divide the top by the bottom. 3/8 is 3 ÷ 8 = 0.375. 7/16 is 7 ÷ 16 = 0.4375. That is all a fraction is — a division waiting to happen — so any fraction of an inch becomes a decimal the same way.

And a decimal back into a fraction?

Multiply by 16 to get sixteenths, then reduce. 0.625 × 16 = 10, so 10/16, which reduces to 5/8. If it does not land on a whole number of sixteenths, it is between marks on the tape.

Why bother when the tape shows fractions?

Because calculators, drawings and specs speak decimals, and your tape speaks sixteenths. Being able to move between the two in your head is what keeps you from stacking rounding errors when you transfer a measurement.

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