Identifying Rational and Irrational Numbers - Determine if the number is rational (R) or irrational (I)

Sep 30, 2026

Uploaded by Ezra

Worksheets for determining whether given values are rational (R) or irrational (I). Each set lists multiple numbers in a mix of decimals, integers, and fractions, then provides an answer key indicating R or I for every item. The material is structured for classroom practice, allowing students to classify each number using rationality rules such as expressibility as a ratio of integers, including repeating/terminating decimals and fractional forms.

LanguageEnglish

CategoryExam

FormatPDF

Pages30

Reading Time1 h 16 min

AccessFree to download

Determine if the number is rational (R) or irrational (I)

Practice problems

Answer key

Identifying Rational and Irrational Numbers Name: Determine if the number is rational (R) or irrational (I). 1) 72.608240 2) 87.580294 3) 63.319683 4) 24.526891 5) 90 6) 36 7) 54 8) 19 9) 6⁄14 10) 4 11) 23⁄24 12) 46⁄8 13) 64 14) 8⁄14 15) 28 16) 82 17) 2.708388 18) 19 19) 55⁄51 20) 15.9380 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Answers Math [www.CommonCoreSheets.com](www.CommonCoreSheets.com) 1 1-10 11-20 95 45 90 40 85 35 80 30 75 25 70 20 65 15 60 10 55 5 50 0 Identifying Rational and Irrational Numbers Name: Answer Key | Determine if the number is rational (R) or irrational (I).
1) 72.608240
2) 87.580294
3) 63.319683
4) 24.526891
5) 90 6) 36 7) 54 8) 19
9) 6⁄14 10) 4
11) 23⁄24
12) 46⁄8 13) 64
14) 8⁄14 15) 28 16) 82
17) 2.708388
18) 19
19) 55⁄51
20) 15.9380

| Answers 1. I 2. I 3. R 4. I 5. R 6. R 7. I 8. I 9. R 10. R 11. R 12. R 13. R 14. R 15. R 16. R 17. R 18. R
19. R
20. R | | --- | --- | Math [www.CommonCoreSheets.com](www.CommonCoreSheets.com) 1 1-10 11-20 95 45 90 40 85 35 80 30 75 25 70 20 65 15 60 10 55 5 50 0 Identifying Rational and Irrational Numbers Name: | Determine if the number is rational (R) or irrational (I). | Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. | | --- | --- | |
RRIR
RRI
II R
IR R | | | 1) 72.608240
2) 87.580294
3) 63.319683
4) 24.526891
5) 90
6) 36
7) 54
8) 19
9) 6⁄14 10) 4
11) 23⁄24
12) 46⁄8 13) 64

| | Math Modified [www.CommonCoreSheets.com](www.CommonCoreSheets.com) 1 1-10 11-13 | 92 | 85 | 77 | 69 | 62 | 54 | 46 | 38 | 31 | 23 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 15 | 8 | 0 | | | | | | | | Identifying Rational and Irrational Numbers Name: Determine if the number is rational (R) or irrational (I). 1) 91.497533 2) 17 3) 29⁄17 4) 48⁄34 5) 88.915724 6) 31⁄15 7) 83.351 8) 70 9) 58.00381 Answers 1. 2. 3. 4. 5. 6. 7. 8. 10) 40⁄1 11) 35 12) 30.227949 13) 3.395862 14) 4⁄47 15) 39 16) 21⁄22 17) 44.602656 18) 45⁄70 19) 10⁄6 20) 19 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Math [www.CommonCoreSheets.com](www.CommonCoreSheets.com) 2 1-10 11-20 95 45 90 40 85 35 80 30 75 25 70 20 65 15 60 10 55 5 50 0 Identifying Rational and Irrational Numbers Name: Answer Key | Determine if the number is rational (R) or irrational (I).
1) 91.497533
2) 17
3) 29⁄17
4) 48⁄34
5) 88.915724
6) 31⁄15
7) 83.351
8) 70
9) 58.00381
10) 40⁄1
11) 35
12) 30.227949
13) 3.395862
14) 4⁄47 15) 39
16) 21⁄22
17) 44.602656
18) 45⁄70
19) 10⁄6 20) 19

| Answers 1. I 2. I 3. R 4. R 5. I 6. R 7. R 8. I 9. R 10. R 11. R 12. R 13. I 14. R 15. I 16. R 17. I 18. R
19. R
20. I | | --- | --- | Math [www.CommonCoreSheets.com](www.CommonCoreSheets.com) 2 1-10 11-20 95 45 90 40 85 35 80 30 75 25 70 20 65 15 60 10 55 5 50 0 Identifying Rational and Irrational Numbers Name: | Determine if the number is rational (R) or irrational (I). | Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. | | --- | --- | |
I I R I
R R R I
I R R R
R | | | 1) 91.497533
2) 17
3) 29⁄17
4) 48⁄34
5) 88.915724
6) 31⁄15

7) 83.351
8) 70

9) 58.00381
10) 40⁄1
11) 35
12) 30.227949
13) 3.395862 | | Math Modified [www.CommonCoreShee

FAQs

How do you determine whether a number is rational or irrational?

Classify each number as rational (R) if it can be expressed as a ratio of two integers; otherwise it is irrational (I). Decimals that terminate or repeat are typically rational, while non-repeating non-terminating decimals are irrational.

What kinds of numbers are included in these problems?

The worksheet includes decimals, integers, and fractions (e.g., numbers written as quotients like a/b or mixed forms such as whole numbers).

What do the letters R and I mean on the answer key?

R stands for rational and I stands for irrational. The answer key marks each numbered item with either R or I.

Sep 30, 2026

Uploaded by Ezra