Repeating decimal facts for kids
A repeating decimal (also called a recurring decimal) is a special kind of decimal number. In these numbers, a digit or a group of digits keeps repeating forever after the decimal point.
Imagine you're trying to share 7 cookies equally among 3 friends. Each friend gets 2 cookies, but there's 1 cookie left. If you cut that cookie into tenths, you'd have 10 tenths. Giving 3 tenths to each friend leaves 1 tenth. If you cut that into hundredths, and so on, you'd keep having a little bit left over.
This is why when you divide 7 by 3, you get 2.333... The digit '3' goes on and on without end. We can write this as 2.3.
The number or group of numbers that repeats is called the repetend (or reptend). In our example, 2.3, the digit '3' is the repetend.
The period length is how many digits are in the repetend. For 2.3, the repetend is just '3', so its period length is 1. If a number was 0.121212..., the repetend would be '12', and the period length would be 2.
How Repeating Decimals Happen
Repeating decimals often appear when you divide one integer (a whole number) by another, and the division doesn't end perfectly.
For example:
- 1 divided by 3 equals 0.333... (repetend '3', period length 1)
- 1 divided by 7 equals 0.142857142857... (repetend '142857', period length 6)
Not all divisions result in repeating decimals. If you divide 1 by 2, you get 0.5, which is a terminating decimal because it ends. This happens when the denominator (the bottom number in a fraction) only has prime factors of 2 or 5.
Why They Are Important
Repeating decimals are a big part of mathematics. They show us that even simple fractions can lead to decimals that go on forever. They are also a key characteristic of rational numbers. A rational number is any number that can be written as a simple fraction (a/b), where 'a' and 'b' are integers and 'b' is not zero. All repeating decimals can be turned back into fractions!
Images for kids
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Formation Rule
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See also
In Spanish: Número decimal periódico para niños
