I'll solve this worksheet on comparing and ordering rational and irrational numbers. Let me work through each problem step by step.
First, I need to understand what rational and irrational numbers are:
- Rational numbers can be expressed as fractions (a/b where a and b are integers, b ≠ 0)
- Irrational numbers cannot be expressed as simple fractions and have non-repeating, non-terminating decimal expansions
Let me start with the first column of problems:
1. 3/5 □ 0.45
- 3/5 = 0.6
- 0.6 > 0.45
- So: 3/5 > 0.45
2. -√15 □ -3.91
- √15 ≈ 3.87 (since 3.87² = 15.0)
- -√15 ≈ -3.87
- -3.87 > -3.91 (because -3.87 is closer to zero)
- So: -√15 > -3.91
3. 87/9 □ √121
- 87/9 = 9.666... (repeating)
- √121 = 11
- 9.666... < 11
- So: 87/9 < √121
4. -1/4 □ -0.25
- -1/4 = -0.25
- So: -1/4 = -0.25
5. √36 □ 61/10
- √36 = 6
- 61/10 = 6.1
- 6 < 6.1
- So: √36 < 61/10
6. 0.07 □ 0.007
- 0.07 = 7/100 = 0.070
- 0.007 = 7/1000 = 0.007
- 0.070 > 0.007
- So: 0.07 > 0.007
7. -3/100 □ -√2
- -3/100 = -0.03
- -√2 ≈ -1.414
- -0.03 > -1.414 (because -0.03 is closer to zero)
- So: -3/100 > -√2
8. 7.56 □ √61
- √61 ≈ 7.81 (since 7.81² = 61.0)
- 7.56 < 7.81
- So: 7.56 < √61
9. -√86 □ -9.3
- √86 ≈ 9.27 (since 9.27² = 86.0)
- -√86 ≈ -9.27
- -9.27 > -9.3 (because -9.27 is closer to zero)
- So: -√86 > -9.3
Now for the ordering problems:
11. 4.5, √17, 17/13, 3.002, √7
- 4.5 = 4.5
- √17 ≈ 4.12
- 17/13 ≈ 1.31
- 3.002 = 3.002
- √7 ≈ 2.65
- Ordering from least to greatest: 17/13, √7, 3.002, √17, 4.5
12. -7/3, -π, -√2, -2.3, -√5
- -7/3 ≈ -2.33
- -π ≈ -3.14
- -√2 ≈ -1.41
- -2.3 = -2.3
- -√5 ≈ -2.24
- Ordering from least to greatest: -π, -7/3, -2.3, -√5, -√2
The completed worksheet should have these answers filled in.
Parent Tip: Review the logic above to help your child master the concept of rational numbers and irrational numbers worksheet.
