Cogito
Grade 7 Math · Chapter 5 · Lesson 4
Terminating and Repeating Decimals
Every fraction becomes one or the other.
10 problems · about 18 minutes · 7.NS.A.2
What this lesson teaches
The child converts a fraction to a decimal and identifies whether it terminates or repeats.
- Every fraction is a division, so every fraction has a decimal form.
- That decimal either terminates or falls into a repeating cycle.
- It must, because there are only finitely many possible remainders.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Why Two Negatives Make a Positive: (−6) × (−4) = ?
Answer 24
Why 24.
Review — Rational Numbers in Problems: −4 + 5 × (−3) = ?
Answer -19
Why −19.
Review — Why a Negative Times a Negative Is Positive: (−9) × (−3) = ?
Answer 27
Why 27.
Warm Up
Straightforward practice. Get the method working first.
3 problemsWrite 3/4 as a decimal.
Answer 0.75
Why 0.75.
Write 1/2 as a decimal.
Answer 0.5
Why Half.
Write 7/10 as a decimal.
Answer 0.7
Why Tenths.
Build It Up
The same ideas with more to keep track of.
2 problemsDoes 1/3 terminate? Answer 1 for yes, 0 for no.
Answer 0
Why 0.333…
Write 5/8 as a decimal.
Answer 0.625
Why 5 ÷ 8.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Quarter: Write 1/4 as a decimal.
Answer 0.25
Why 0.25, which terminates.
The Fifth: Write 3/5 as a decimal.
Answer 0.6
Why 0.6, which terminates.