Decimal Fractions

Q1: Convert each of the sets of unlike decimals into like decimals:

i. 9.4, 65.83, 0.065

Step 1: Find the maximum number of decimal places = 3 (from 0.065)
Step 2: Convert all numbers to 3 decimal places by adding zeroes:
9.4 → 9.400
65.83 → 65.830
0.065 → 0.065
Answer: 9.400, 65.830, 0.065

ii. 0.5, 7.573, 4.26, 8.4

Step 1: Max decimal places = 3 (from 7.573)
Step 2: Add zeroes to convert:
0.5 → 0.500
7.573 → 7.573
4.26 → 4.260
8.4 → 8.400
Answer: 0.500, 7.573, 4.260, 8.400

iii. 1.2, 0.06, 3.5, 6.38

Step 1: Max decimal places = 2 (from 0.06, 6.38)
Step 2: Convert all to 2 decimal places:
1.2 → 1.20
0.06 → 0.06
3.5 → 3.50
6.38 → 6.38
Answer: 1.20, 0.06, 3.50, 6.38

iv. 2.8, 16.85, 64.056, 143.625

Step 1: Max decimal places = 3 (from 64.056 and 143.625)
Step 2: Convert all to 3 decimal places:
2.8 → 2.800
16.85 → 16.850
64.056 → 64.056
143.625 → 143.625
Answer: 2.800, 16.850, 64.056, 143.625

Q2: Fill in the place holders with > or < :

i. 63.4 ___ 36.85

Step 1: Compare whole numbers: 63 > 36
Answer: 63.4 > 36.85

ii. 4.805 ___ 4.85

Step 1: Make like decimals: 4.805 vs 4.850
Step 2: Compare digit by digit → 4.805 < 4.850
Answer: 4.805 < 4.85

iii. 8.23 ___ 8.32

Step 1: Compare tenths place: 2 < 3
Answer: 8.23 < 8.32

iv. 5.06 ___ 5.006

Step 1: Make like decimals: 5.060 vs 5.006
Step 2: Compare hundredths: 6 > 0
Answer: 5.06 > 5.006

v. 7.86 ___ 7.806

Step 1: Make like decimals: 7.860 vs 7.806
Step 2: Compare hundredths: 6 > 0
Answer: 7.86 > 7.806

vi. 0.98 ___ 1

Step 1: Compare whole numbers: 0 < 1
Answer: 0.98 < 1

Q3: Arrange the following decimals in ascending order:

i. 3.6, 4.2, 3.57, 4.18, 3.06, 4.08

Step 1: Convert all to 2 decimal places:
3.60, 4.20, 3.57, 4.18, 3.06, 4.08
Step 2: Arrange from smallest to greatest:
3.06 < 3.57 < 3.60 < 4.08 < 4.18 < 4.20
Answer: 3.06 < 3.57 < 3.6 < 4.08 < 4.18 < 4.2

ii. 5.37, 3.57, 3.5, 5.3, 5.7, 3.07

Step 1: Convert all to 2 decimal places:
5.37, 3.57, 3.50, 5.30, 5.70, 3.07
Step 2: Arrange:
3.07 < 3.50 < 3.57 < 5.30 < 5.37 < 5.70
Answer: 3.07 < 3.5 < 3.57 < 5.3 < 5.37 < 5.7

iii. 0.7, 0.007, 0.07, 7.7, 7.07, 0.77

Step 1: Convert all to 3 decimal places:
0.700, 0.007, 0.070, 7.700, 7.070, 0.770
Step 2: Arrange:
0.007 < 0.070 < 0.700 < 0.770 < 7.070 < 7.700
Answer: 0.007 < 0.07 < 0.7 < 0.77 < 7.07 < 7.7

iv. 2.2, 2.02, 0.22, 0.02, 0.202, 2.002

Step 1: Convert all to 3 decimal places:
2.200, 2.020, 0.220, 0.020, 0.202, 2.002
Step 2: Arrange:
0.020 < 0.202 < 0.220 < 2.002 < 2.020 < 2.200
Answer: 0.02 < 0.202 < 0.22 < 2.002 < 2.02 < 2.2

v. 76.8, 68.7, 86.7, 87.6, 78.6, 7.86

Step 1: Convert all to 2 decimal places:
76.80, 68.70, 86.70, 87.60, 78.60, 7.86
Step 2: Arrange:
7.86 < 68.70 < 76.80 < 78.60 < 86.70 < 87.60
Answer: 7.86 < 68.7 < 76.8 < 78.6 < 86.7 < 87.6

Q4: Arrange the following decimals in descending order:

i. 6.6, 0.06, 0.6, 0.006, 6.66

Step 1: Convert all to 3 decimal places:
6.600, 0.060, 0.600, 0.006, 6.660
Step 2: Arrange from greatest to smallest:
6.660 > 6.600 > 0.600 > 0.060 > 0.006
Answer: 6.66 > 6.6 > 0.6 > 0.06 > 0.006

ii. 3.3, 3.03, 0.33, 33.3, 0.303, 30.3

Step 1: Convert all to 3 decimal places:
3.300, 3.030, 0.330, 33.300, 0.303, 30.300
Step 2: Arrange from greatest to smallest:
33.300 > 30.300 > 3.300 > 3.030 > 0.330 > 0.303
Answer: 33.3 > 30.3 > 3.3 > 3.03 > 0.33 > 0.303

iii. 2.9, 3.6, 9.2, 6.3, 3.06, 6.03

Step 1: Convert to 2 decimal places:
2.90, 3.60, 9.20, 6.30, 3.06, 6.03
Step 2: Descending order:
9.20 > 6.30 > 6.03 > 3.60 > 3.06 > 2.90
Answer: 9.2 > 6.3 > 6.03 > 3.6 > 3.06 > 2.9

iv. 77.7, 0.7, 7.7, 0.07, 7.07, 7.77

Step 1: Convert to 2 decimal places:
77.70, 0.70, 7.70, 0.07, 7.07, 7.77
Step 2: Descending order:
77.70 > 7.77 > 7.70 > 7.07 > 0.70 > 0.07
Answer: 77.7 > 7.77 > 7.7 > 7.07 > 0.7 > 0.07

v. 7.35, 3.75, 5.3, 3.57, 5.37, 5.75

Step 1: All are already to 2 decimal places.
Step 2: Descending order:
7.35 > 5.75 > 5.37 > 5.3 > 3.75 > 3.57
Answer: 7.35 > 5.75 > 5.37 > 5.3 > 3.75 > 3.57