Fractions, decimals & percentages

A fraction, a decimal and a percentage are three ways of writing the same number. 1/2 = 0.5 = 50% all describe exactly half of something. Percent literally means "out of 100", so a percentage is just a fraction with a hidden denominator of 100: 50% means 50/100. Knowing this is what lets you move between all three.

A fraction bar is a division sign, so to turn a fraction into a decimal you divide the top by the bottom: 3/4 = 3 ÷ 4 = 0.75. To go the other way, read the place value. 0.35 has two decimal places — hundredths — so it is 35/100, which cancels down to 7/20. Always simplify the fraction by dividing the top and bottom by their highest common factor.

To change a decimal into a percentage, multiply by 100 (the digits shift two places left): 0.5 = 50% and 0.07 = 7%. To change a percentage back into a decimal, divide by 100: 45% = 0.45. A handy shortcut is that the percentage is simply the decimal with the point moved two places.

The quickest route is often to make an equivalent fraction over 100. Since 7/20 = 35/100, you can read off 7/20 = 35% straight away. If the denominator does not divide neatly into 100, turn the fraction into a decimal first and then multiply by 100: 3/5 = 0.6 = 60%. It is worth memorising the everyday ones — 1/2 = 50%, 1/4 = 25%, 3/4 = 75%, 1/5 = 20% — because they come up again and again.

You cannot compare a fraction with a decimal while they are in different costumes. Convert them to the same form first — usually decimals are the easiest. To compare 3/8 and 0.4, turn the fraction into a decimal: 3/8 = 0.375. Now it is clear that 0.375 < 0.4, so 0.4 is the larger value. Same value, same form, then compare.

When a question asks for a decimal, type it like 0.75. When it asks for a percentage, type just the number — 35, not 35%. When it asks for a fraction, type it with a slash, like 7/20, and give it in its simplest form. You may type a fraction answer as a decimal if you prefer; both are accepted.