How to Convert Between Fractions, Decimals and Percentages

The method, step by step

1. 01

   Fraction to decimal: divide the top by the bottom

   3/8 → 3 ÷ 8 = 0.375

   A fraction is a division that has not been carried out yet, so the conversion is not a new rule — it is finishing the sum the fraction was already describing. Reading 3/8 aloud as "three divided by eight" removes the guesswork about which number goes inside the division.

2. 02

   Decimal to percentage: multiply by 100

   0.375 × 100 = 37.5%

   Per cent means per hundred, so a percentage is the decimal measured on a scale of a hundred rather than of one. Multiplying by 100 moves the digits two places left across the decimal point, which is why 0.375 becomes 37.5 rather than 3.75.

3. 03

   Percentage to decimal: divide by 100

   37.5% → 37.5 ÷ 100 = 0.375

   This is the step almost every percentage calculation needs first, because a calculator cannot multiply by a per cent sign. Getting 45% to 0.45 before touching anything else turns "45% of 260" into a single multiplication.

4. 04

   Decimal to fraction: use place value, then simplify

   0.375 = 375/1000 = 3/8

   The last digit tells you the denominator: three decimal places means thousandths, so 0.375 is 375 thousandths before anything is cancelled. Simplifying is a separate job from converting, and separating them stops the two being confused when the cancelling is awkward.

5. 05

   Percentage to fraction: write it over 100 and simplify

   45% = 45/100 = 9/20

   Because per cent already means "out of a hundred", the fraction is written down before any work is done. Both 45 and 100 divide by 5, giving 9/20. The simplifying is where the marks are lost, not the writing down.

6. 06

   Check by converting back the other way

   9/20 → 9 ÷ 20 = 0.45 → 0.45 × 100 = 45% ✓

   Every one of these conversions is reversible, which makes checking free. Running the answer back to the form you started in catches a misplaced decimal point immediately, and a misplaced decimal point is the single most common error in this topic.

01

They are one number in three costumes

A fraction, a decimal and a percentage are not three topics. They are three notations for the same quantity, chosen for convenience: fractions for exact parts, decimals for calculating, percentages for comparing. Once that is genuinely believed, the conversions stop being six rules to memorise and become two moves used in both directions.

It helps to hold a short table of equivalents in memory rather than deriving the common ones every time. These come up constantly, and recalling them frees attention for the part of the question that is actually being tested.

• 1/2 = 0.5 = 50%
• 1/4 = 0.25 = 25%
• 3/4 = 0.75 = 75%
• 1/5 = 0.2 = 20%
• 1/8 = 0.125 = 12.5%
• 3/8 = 0.375 = 37.5%
• 1/3 = 0.333… = 33.3% (to 1 d.p.)
• 7/20 = 0.35 = 35%

02

When the decimal does not stop

Not every fraction gives a decimal that terminates. Dividing 2 by 3 gives 0.6666… continuing indefinitely, written 0.6 with a dot above the 6. As a percentage it is 66.7% to one decimal place, and rounding it is a decision to state rather than to hide.

A fraction terminates as a decimal only when its denominator, once fully simplified, has no prime factors other than 2 and 5. That is why eighths and twentieths terminate and thirds and sevenths do not. Knowing this in advance saves a student from dividing forever and assuming they have made a mistake.

03

Ordering a mixed list

Questions that ask a student to put 0.6, 5/8 and 62% in order are testing exactly one thing: whether the student converts everything to a single form first. Trying to compare across three notations is where the errors come from.

Decimals are usually the easiest common ground, because comparing them is a digit-by-digit read from the left. Here 5/8 = 0.625, 62% = 0.62 and 0.6 stays as it is, so the order is 0.6, then 62%, then 5/8. The working is short once the decision to convert is made.

04

How we teach this

We teach the two conversions and their reverses rather than six separate procedures, because students who learn six rules apply the wrong one under pressure. Naming the move — "divide top by bottom", "multiply by a hundred" — and then running it backwards is what makes it hold.

The equivalents table is memorised deliberately in our middle-grade classes. It is a small amount of learning that removes a large amount of arithmetic later, particularly in percentage and probability questions where the fraction is a step rather than the answer.