Math 7 · Unit 3, Lesson 6: Fractions to Decimals · Tile 3 of 3
Stop or Repeat?
Mixed numbers, negatives, and calling it ahead of time
Every fraction stops or repeats
Every fraction of integers turns into a decimal that stops or repeats. That works the other way too: every decimal that stops or repeats is a rational number. For a mixed number, keep the whole number and divide just the fraction part.
The decimal form of every rational number either terminates or eventually repeats.
No fraction makes a decimal that goes on forever with no pattern. It stops, or it loops.
Call it ahead of time
A pattern to notice, not a rule to memorize. Write the fraction in simplest form. Look at the bottom (denominator). If its only factors are 2s and 5s, the decimal stops, because 10 is 2 × 5. If it has any other factor, like 3, 7, or 11, the decimal repeats.
| Fraction | The bottom | So it |
|---|---|---|
| 38 | 8 = 2 × 2 × 2 | stops |
| 720 | 20 = 2 × 2 × 5 | stops |
| 56 | 6 = 2 × 3 | repeats |
| 17 | 7 | repeats |
Watch it work
NC standard: NC.7.NS.2.