Decimal & Percent Notation

You can turn any decimal into a fraction by using place value. The digits after the decimal point tell you the denominator, which is the bottom number of the fraction.

Try 0.07. The 7 is in the hundredths place, so 0.07 means 7 hundredths. Write the 7 on top and 100 on the bottom: 0.07 = 7/100.

Try 2.1. The number before the point stays a whole number, so we keep the 2. The 1 is in the tenths place, so we add 1/10. That gives 2 and 1/10.

Try 0.6. The 6 is in the tenths place, so 0.6 = 6/10. You can simplify that to 3/5 if you like, but 6/10 is already correct.

Count how many digits are after the point. One digit means tenths, so the denominator is 10. Two digits mean hundredths, so the denominator is 100. Three digits mean thousandths, so the denominator is 1000. The digits themselves go on top.

Written form means saying a number with words. Here is how to read 3.405.

First look at the place value chart. The 3 is in the ones place, the 4 is in the tenths place, the 0 is in the hundredths place, and the 5 is in the thousandths place.

Step one: read the part before the point. That is just three.

Step two: say and for the decimal point.

Step three: read the digits after the point as a team, not one at a time. After the point we have 405, which is four hundred five. Then say the place of the last digit. The last digit, 5, is in the thousandths place.

So 3.405 is three and four hundred five thousandths.

Watch out for zeros. In 3.045 the 0 after the point still gets counted as a place, so you say three and forty-five thousandths. The zero is there, it just does not get its own word. With a little practice you will read big decimals easily.

Percents, fractions, and decimals are all just different ways of writing the same number. Ben ate 50% of the pizza, or 1/2 of the pizza, or 0.5 of the pizza. All three mean the exact same thing.

To change a percent to a decimal, divide by 100. That moves the point two places to the left. So 18% becomes 0.18.

To change a decimal to a percent, multiply by 100. That moves the point two places to the right. So 0.18 becomes 18%.

To change a percent to a fraction, write the number over 100. So 18% is 18/100. You can simplify it: divide the top and bottom by 2 to get 9/50.

To change a fraction to a decimal, divide the top by the bottom. So 1/2 is 1 divided by 2, which is 0.5.

Here is the same number in all three costumes: 25% = 25/100 = 0.25. Once you see that they match, switching between them feels like a game.

A percent is a way to count out of 100. The word comes from Latin and means per one hundred.

If a square is split into 100 tiny squares and 43 of them are shaded, then 43% is shaded. The 43 is how many, and the % sign says out of 100.

Some percents are easy to picture. 100% means the whole thing. 50% means half. 25% means one quarter. 10% means one tenth, which is one out of every ten.

You can turn any percent into a fraction by writing it over 100. 75% is 75/100, which simplifies to 3/4.

You can also turn a percent into a decimal. 75% means 75 divided by 100, which is 0.75.

And you can go the other way too. 0.3 means 3 tenths, which is 30 out of 100, so 0.3 = 30%.

Percents are everywhere: sale signs, test scores, and how much of your chores are done. When you can read them, the world makes more sense.

What is the difference between a terminating decimal and a repeating decimal? A terminating decimal is one that ends. 33/100 is 0.33, which stops after two digits. A repeating decimal goes on forever. 1/3 is 0.3333 and the threes never stop. We can draw a bar over the 3 to show it repeats: 0.3 with a bar on top.

Can every fraction become a decimal? Yes. Divide the top number by the bottom number and you get either a terminating decimal like 0.75 or a repeating decimal like 0.333.

Is 0.5 the same as 5%? No, and this trick catches many people. 0.5 is a half, and a half is 50 out of 100, so 0.5 = 50%. To turn a decimal into a percent, move the point two places to the right, not one. 0.5 becomes 50, and 0.05 becomes 5.

Which should I use, a fraction, a decimal, or a percent? They are the same value wearing different costumes. Use a percent for things out of 100, like test scores. Use a decimal for measuring. Use a fraction for parts of a whole, like slices of pizza.