Fraction-Decimal Equivalents

A decimal is just a fraction wearing a different outfit. The digits after the decimal point tell you the fraction.

The first digit after the point counts tenths. So 0.5 means 5 tenths, and you can write that as 5/10. And 5/10 is the same as 1/2.

The second digit counts hundredths. So 0.25 means 25 hundredths, which is 25/100. If you shade a 100 square grid, 25 shaded squares is exactly one quarter, so 25/100 = 1/4.

Try 0.75. It means 75 hundredths, or 75/100. Split the grid into 4 equal groups and 3 of them are shaded, so 75/100 = 3/4.

A decimal point is a little signpost. It tells you where the whole numbers stop and the tenths begin.

Say you have the fraction 5/10. That means 5 tenths. To write it as a decimal, put a 0 before the point for the whole number part, then a 5 in the tenths place: 0.5.

This is why 1/2 = 0.5. If you multiply the top and bottom of 1/2 by 5, you get 5/10, and 5/10 is 0.5.

The same idea works for hundredths, the next place over. The fraction 25/100 has 25 hundredths, so it needs two digits after the point: 0.25. And 25/100 is the same as 1/4.

When you read a decimal out loud, the word and marks the decimal point. Three and four tenths is 3.4. For amounts less than 1, you just say the decimal part: 0.5 is five tenths, and 0.75 is seventy five hundredths.

Fractions and decimals are two names for the same amount. Here are two friendly ways to turn a fraction into a decimal.

Way one: make the bottom number 10 or 100. For 1/2, multiply the top and bottom by 5 to get 5/10, which is 0.5. For 1/4, multiply the top and bottom by 25 to get 25/100, which is 0.25. For 3/4, multiply by 25 to get 75/100, which is 0.75.

Way two: divide the top number by the bottom number. For 1/4, ask how many 4s fit into 1. It is less than 1, so think of 1 as 1.00. Four fits into 100 exactly 25 times, so the answer is 0.25. Both ways give you the same answer, so pick the one you like.

A handy tip: quarters are easy because 100 splits into 4 equal groups of 25. That is why every quarter comes out as a clean hundredth, like 0.25, 0.50, and 0.75.

Decimals are numbers that use a point to show parts of a whole. The places after the point have special names.

The first place after the point is tenths. Ten tenths make one whole, so 0.1 is one tenth and 0.5 is five tenths. Five tenths is the same as 5/10, which simplifies to 1/2.

The second place is hundredths. One hundred hundredths make one whole, so 0.25 is twenty five hundredths and 0.75 is seventy five hundredths. In fraction form those are 25/100 and 75/100.

You can picture every decimal on a 100 square grid. Shade 25 squares and you have shown 0.25. That same shading is one of four equal parts, so 0.25 = 1/4. Shade 75 squares and you have three of four parts, so 0.75 = 3/4.

Turning a fraction into a decimal is easier than it looks. Here are the friendliest ways.

Use a power of ten. If you can make the bottom number 10 or 100, the decimal writes itself. 1/2 becomes 5/10, which is 0.5. 1/4 becomes 25/100, which is 0.25. 3/4 becomes 75/100, which is 0.75.

Use division. Put the top number inside a division box and the bottom number outside. Dividing 1 by 4 gives 0.25, because 4 fits into 1.00 exactly 0.25 times. Every fraction is really a division problem waiting to happen.

Use something you already know. A quarter is 25 cents, and there are 100 cents in a dollar. That is a clue that 1/4 = 25/100 = 0.25. Three quarters would be 75 cents, so 3/4 = 0.75.

Check your work with a grid. Shade the fraction on a 100 square grid and read off the hundredths. If the shading and the decimal agree, you got it right.