Seventh Grade · Math · week 13

Terminating and repeating decimals

Determine whether a fraction converts to a terminating or a repeating decimal, and write repeating decimals using correct notation.

Every rational number's decimal either STOPS (terminating, like 0.25) or REPEATS a pattern forever (like 0.3333...). Both are completely normal decimal forms for a fraction.

A fraction in simplest form terminates only when its denominator's prime factors are just 2s and 5s. If any other prime factor (like 3 or 7) is in the denominator, the decimal repeats instead.

Write a repeating decimal by showing the repeating block followed by "...", and naming which digit or digits repeat, like 0.1666... (the 6 repeats forever).

📋 For the teacher
Teach it (10–15 min):
  • Have them factor the denominator first, every time, before dividing -- it predicts the answer before any long division happens.
  • Practice long division far enough to actually SEE a digit start repeating, rather than just being told the rule.
  • Write repeating decimals consistently with "..." and a note naming the repeating digit(s).
  • Point out this never changes for negative fractions -- just convert the positive version and reattach the sign.
Talk about it:
  • How can you predict whether a fraction terminates just by looking at its denominator?
  • Why does 1/3 repeat but 1/4 does not?
  • What repeats in the decimal for 5/6, and why?

Mastery looks like: They correctly classify a fraction as terminating or repeating using the denominator's factors, and convert it accurately.

Common stumbles: Forgetting to simplify the fraction before checking the denominator's factors; stopping long division before a repeating digit actually appears.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

FractionsSlice bars and circles into equal parts and compare them.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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