Irrational Numbers Worksheets - 15 Worksheets Library - Free Printable

Let’s go through each fraction one by one. We’re told:
> A rational number p/q is a terminating decimal only when the prime factors of q (after simplifying the fraction) are 2 and/or 5 only.

So our plan:
1. Simplify each fraction if needed.
2. Look at the denominator after simplifying.
3. Factor the denominator into primes.
4. If it has ONLY 2s and/or 5s → terminating decimal ✔
If it has any other prime (like 3, 7, 11, etc.) → NOT terminating ✘

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Let’s do them:

1) 3/8
Denominator = 8 = 2×2×2 → only 2s → ✔ Terminating

2) 12/35
Already simplified? 12 and 35 share no common factors.
35 = 5 × 7 → has 7 → ✘ Not terminating

3) 17/55
17 is prime, doesn’t divide 55.
55 = 5 × 11 → has 11 → ✘ Not terminating

4) 9/16
16 = 2⁴ → only 2s → ✔ Terminating

5) 5/18
18 = 2 × 3² → has 3 → ✘ Not terminating

6) 8/30
Simplify first: divide numerator and denominator by 2 → 4/15
15 = 3 × 5 → has 3 → ✘ Not terminating

7) 45/80
Simplify: both divisible by 5 → 9/16
16 = 2⁴ → only 2s → ✔ Terminating

8) 15/50
Simplify: divide by 5 → 3/10
10 = 2 × 5 → only 2 and 5 → ✔ Terminating

9) 18/40
Simplify: divide by 2 → 9/20
20 = 2² × 5 → only 2 and 5 → ✔ Terminating

10) 20/30
Simplify: divide by 10 → 2/3
3 is prime → not 2 or 5 → ✘ Not terminating

11) 44/60
Simplify: divide by 4 → 11/15
15 = 3 × 5 → has 3 → ✘ Not terminating

12) 10/35
Simplify: divide by 5 → 2/7
7 is prime → not 2 or 5 → ✘ Not terminating

13) 45/160
Simplify: divide by 5 → 9/32
32 = 2⁵ → only 2s → ✔ Terminating

14) 35/60
Simplify: divide by 5 → 7/12
12 = 2² × 3 → has 3 → ✘ Not terminating

15) 35/100
Simplify: divide by 5 → 7/20
20 = 2² × 5 → only 2 and 5 → ✔ Terminating

16) 8/28
Simplify: divide by 4 → 2/7
7 is prime → not 2 or 5 → ✘ Not terminating

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Now let’s list which ones are terminating decimals:

✔ Terminating: 1, 4, 7, 8, 9, 13, 15
✘ Not terminating: 2, 3, 5, 6, 10, 11, 12, 14, 16

Final Answer:
Terminating decimals: 1, 4, 7, 8, 9, 13, 15