Percentage and decimal equivalents

A percentage is just a way of saying how many parts out of 100. Once you see that, converting is easy.

Way 1: Start with a decimal. Move the decimal point two places to the right and add the percent sign. So 0.75 becomes 75%. Moving two places is the same as multiplying by 100, because percent means out of 100.

Way 2: Start with a fraction. First turn the fraction into a decimal, then do Way 1. For example, 3/4 = 0.75, and 0.75 becomes 75%.

Way 3: Estimate in your head. If there is no calculator nearby, you can split the number into friendly pieces. To find 15% of a bill, take 10% first, then add half of that again, because half of 10% is 5%. This works because percentages can be added together.

A handy trick: 10% of something is just the something with the digits moved one place smaller. Ten percent of 80 is 8, and ten percent of 6 is 0.6. From there you can build bigger percentages by adding.

The same amount can be written in three different costumes: as a fraction, as a decimal, or as a percentage. Learning to swap between them lets you pick the costume that makes each problem easiest.

Start with the fractions you know well. One half is 0.5 or 50%. One quarter is 0.25 or 25%. One fifth is 0.2 or 20%. Once these are memorized, the rest come free, because two fifths is just double one fifth: 0.4 or 40%. Four fifths is 0.8 or 80%.

Fractions with denominators of 10 or 100 are the friendliest of all. Seven tenths is 0.7, and seven hundredths is 0.07. The number of zeros in the denominator tells you how many places the decimal needs.

Practice spotting the same value in all three forms. If a square is half shaded, you can call it 1/2, 0.5, or 50%, and you are right every time.

This interactive tool shows you that fractions, decimals and percentages are three names for the same thing.

On the screen you see a shape, like a square or a circle, split into equal parts. Some parts are colored in. The tool labels the colored part three ways at once: as a fraction, as a decimal, and as a percentage.

Try dragging the slider to color in more parts. Watch how all three numbers change together. When half the shape is colored, the tool shows 1/2, 0.5 and 50% side by side. When one part out of five is colored, it shows 1/5, 0.2 and 20%.

Play until you can guess one of the numbers before you look. If you see the decimal 0.75, can you say the fraction and the percentage? This game of guessing is the fastest way to make the three forms feel like old friends.

A percentage always means out of 100. That single idea lets you turn any percentage into a decimal or a fraction.

To turn a percentage into a decimal, divide by 100. Dividing by 100 moves the decimal point two places to the left. So 25% becomes 0.25, and 80% becomes 0.80, which is just 0.8.

To turn a percentage into a fraction, write it over 100 and then simplify. Sixty percent becomes 60/100. Both numbers divide by 20, so it simplifies to 3/5.

To go the other way, from a decimal to a percentage, move the point two places right and add the percent sign. The decimal 0.2 becomes 20%.

Try these in your head: 50% is 1/2, 25% is 1/4, and 10% is 1/10. These three are worth knowing by heart because they come up everywhere, from test scores to sale signs.

A decimal is another way to write a fraction whose denominator is a power of ten, like 10, 100 or 1000.

The first place after the decimal point counts tenths. The second place counts hundredths, and the third counts thousandths. So 0.3 means 3/10, and 0.03 means 3/100. Those two numbers look alike but they are very different, so always count the places carefully.

This is why converting is so simple for fractions with denominators of 10, 100 or 1000. To write 7/10 as a decimal, you only need to say what you see: seven tenths, which is 0.7. To write 7/100, say seven hundredths, which is 0.07.

Other fractions take one small extra step. To convert 3/4, first rewrite it with a denominator of 100. Since 4 x 25 = 100, multiply the top and bottom by 25 to get 75/100, which is 0.75.