Finding Repeating Decimals - Math Worksheet - Determine R or T

Sep 30, 2026

Uploaded by Logic

Worksheet and answer-key materials focused on converting fractions and division expressions into decimals and classifying them as repeating (R) or terminating (T). The guide explains the rule for terminating decimals: a simplified denominator whose prime factors include only 2 and 5. It also explains that any prime factor other than 2 or 5 produces a repeating decimal. A set of numbered problems is provided, with corresponding R/T classifications.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Determine R or T (Repeating or Terminating)

Rule for Terminating Decimals

Problems to Classify

Finding Repeating Decimals Name: | Determine if each problem when converted to a decimal will result in a repeating (R) or | | | | | | | | | Answers | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | |
terminating (T) decimal.
A fraction will result in a terminating decimal if the prime factors of the simplified denominator contain only 2s or 5s (or only 2s and 5s) .
6⁄40 = 3⁄20 = 2×2×5 = 0.15
A fraction will result in a repeating decimal if the prime factors of the simplified denominator contain any prime factor other than 2 or 5.
5⁄42 = 2×3×7 = 0.1190476 | | | | | | | | | 1.
2.
3.
4. | | | | | | |
1) 2⁄3 = | | | | | | | | | 5.
6. | | | | | | | 2) 19 ÷ 8 = | | | | | | | | | 7. | | | | | | | 3) 86 ÷ 20 = | | | | | | | | | 8. | | | | | | | 4) 102 ÷ 19 = | | | | | | | | | 9. | | | | | | | 5) 135 ÷ 17 = | | | | | | | | | 10. | | | | | | | 6) 5⁄27 = | | | | | | | | | 11. | | | | | | | 7) 11⁄13 = | | | | | | | | | 12. | | | | | | | 8) 164 ÷ 16 = | | | | | | | | | | | | | | | | 9) 11⁄30 =
10) 79 ÷ 24 = | | | | | | | | | 13.
14. | | | | | | | 11) 2⁄15 = | | | | | | | | | 15. | | | | | | | 12) 243 ÷ 26 = | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 13) 3⁄18 = | | | | | | | | | | | | | | | | 14) 8⁄22 = | | | | | | | | | | | | | | | | 15) 144 ÷ 14 = | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Math | | [www.CommonCoreSheets.com](www.CommonCoreSheets.com) | 1 | 1-10
11-15 | 93 | 87 | 80 | 73 | 67 | 60 | 53 | 47 | 40 | 33 | | | | | | | 27 | 20 | 13 | 7 | 0 | | | | | | Finding Repeating Decimals Name: Answer Key | Determine if each problem when converted to a decimal will result in a repeating (R) or | | | | | | | | Answers | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | |
terminating (T) decimal.
A fraction will result in a terminating decimal if the prime factors of the simplified denominator contain only 2s or 5s (or only 2s and 5s) .
6⁄40 = 3⁄20 = 2×2×5 = 0.15
A fraction will result in a repeating decimal if the prime factors of the simplified denominator contain any prime factor other than 2 or 5.
5⁄42 = 2×3×7 = 0.1190476 | | | | | | | | 1. R
2. T
3. T
4. R
5. R | | | | | | | | 1) 2⁄3 = 3
2) 19 ÷ 8 = 2×2×2
3) 86 ÷ 20 = 2×5
4) 102 ÷ 19 = 19
5) 135 ÷ 17 = 17
6) 5⁄27 = 3×3×3
7) 11⁄13 = 13
8) 164 ÷ 16 = 2×2
9) 11⁄30 = 2×3×5
10) 79 ÷ 24 = 2×2×2×3
11) 2⁄15 = 3×5 | | | | | | | | 6. R
7. R
8. T
9. R
10. R
11. R
12. R
13. R
14. R
15. R | | | | | | | | 12) 243 ÷ 26 = 2×13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 13) 3⁄18 = 2×3 | | | | | | | | | | | | | | | | 14) 8⁄22 = 11 | | | | | | | | | | | | | | | | 15) 144 ÷ 14 = 7 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Math | [www.CommonCoreSheets.com](www.CommonCoreSheets.com) | 1 | 1-10
11-15 | 93 | 87 | 80 | 73 | | 67 | 60 | 53 | 47 | 40 | 33 | | | | | | 27 | 20 | 13 | 7 | | 0 | | | | | | Finding Repeating Decimals Name: | Determine if each problem when converted to a decimal will result in a repeating (R) or

terminating (T) decimal.
A fraction will result in a terminating decimal if the prime factors of the simplified denominator contain only 2s or 5s (or only 2s and 5s) .
6⁄40 = 3⁄20 = 2×2×5 = 0.15
A fraction will result in a repeating decimal if the prime fact

FAQs

How do you determine whether a fraction becomes a terminating decimal?

Reduce the fraction, then factor the simplified denominator. If its prime factors contain only 2s and/or 5s, the decimal terminates.

When will a decimal representation be repeating?

A repeating decimal occurs if the simplified denominator contains any prime factor other than 2 or 5.

Which examples in the worksheet are classified as repeating (R) or terminating (T)?

The provided list of problems is assigned an R or T label in the answer key, including items like 2/3 as R and 19 ÷ 8 as T.

Sep 30, 2026

Uploaded by Logic