Worksheet Solutions: Decimals
Q1: Compare the numbers. Add: > or < or =
(i) 7.1 ____ 95.1
Ans: 7.1< 95.1
Explanation: 95.1 has a larger whole number part (95) than 7.1 (7), so 7.1 < 95.1.
(ii) 0.6 ____ 7.07
Ans: 0.6< 7.07
Explanation: 7.07 has whole number part 7 while 0.6 has whole number 0, so 0.6 < 7.07.
(iii) 92.8 ____ 79.7
Ans: 92.8> 79.7
Explanation: 92.8 has whole number 92 which is greater than 79, so 92.8 > 79.7.
(iv) 5.55 ____ 0.7
Ans: 5.55> 0.7
Explanation: 5.55 has whole number 5 and 0.7 has whole number 0, so 5.55 > 0.7.
(v) 25.6 ____ 7.5
Ans: 25.6> 7.5
Explanation: 25.6 (whole 25) is bigger than 7.5 (whole 7), so 25.6 > 7.5.
Q2: Solve the following questions
1. Add
i) 8416 + 0.28 + 1.489
ii) 74.906 + 0 .01 + 42
iii) 13.6 + 42.18
2. Subtract
i) 16.001 - 12.984
ii) 0.001 from 0.01
iii) 346.8912 - 29.98764
3. Divide
i) 2807 by 1.4
2807/1.4 = 28070 / 14
ii) 0.64 by 0.14208
Sol:
iii) 2.303 by 329
Sol:
iv) 315.6 by 0.789
4. Multiply
i) 84.78 x 0.612
Product = 84.78 × 0.612 = 51.88536
ii) 98.47 x 0 .7
Product = 98.47 × 0.7 = 68.929
iii) 0.8842 x 0.002
Product = 0.8842 × 0.002 = 0.0017684
Q3: Convert the following decimal into fractions (reduce, if possible)
(a) 0.25
Sol: 0.25 = 25/100 = 1/4
(b) 0.66
Sol: 0.66 = 66/100 = 33/50
(c) 2.4
Sol: 2.4 = 24/10 = 12/5
(d) 42.875
Sol: 42.875 = 42875/1000 = 1715/40 = 343/8
(e) 27.216
Sol: 27.216 = 27216/1000 = 3402/125
(f) 0.141
Sol: 0.141 = 141/1000
Q4: Convert the following fractions to decimals.
In order to convert fraction into decimal, we can simply divide the two and the quotient is the required answer.
(a) 77/80
Sol:
77 ÷ 80 = 0.9625
(b) 12/16
Sol:
12/16 = 3/4 and 3 ÷ 4 = 0.75
(c) 13/8
Sol:
13 ÷ 8 = 1.625
(d)19/25
Sol:
19 ÷ 25 = 0.76
Sol: It can be written as (96 + 1)/8 = 97/8
97 ÷ 8 = 12.125
Sol: It can be written as (36+1) / 4 = 37/4
37 ÷ 4 = 9.25
Q5: Write the following in form of decimal numbers.
(i) 
(ii) 
(iii) 
(iv) Eighteen hundredths +8 thousandths
(v)99 hundredths + 89
Sol: (i) 300 + 1/10 + 10 + 9 + 67 thousandths
Now, 67 thousandths = 67/1000
So, 300 + 0.1 + 10 + 9 + 0.067
Arranged in descending order = 300 + 10 + 9 + 0.1 + 0.067 = 319.167
Therefore, the correct decimal number is 319.167
(ii) 8/100 + 3/10 + 5/1000 + 90 + 3
Now, simplify fraction form according to the above figure
8/100 + 3/10 + 5/1000 + 90 + 3 = 0.08 + 0.3 + 0.005 + 90 + 3
Arranged in descending order = 90 + 3 + 0.3 + 0.08 + 0.005 = 93.385
Therefore, the correct decimal number is
8/100 + 3/10 + 5/1000 + 90 + 3 = 93.385
(iii)5/100 + 7 thousandths + 2 + 400 + 4000
Simplify fraction form according to the above figure. 7 thousandths = 7/1000
So, 5/100 + 7/1000 + 2 + 400 + 4000 = 0.05 + 0.007 + 2 + 400 + 4000
Arranged in descending order = 4000 + 400 + 2 + 0.05 + 0.007 = 4402.057
Therefore, the correct decimal number is 4402.057
(iv) Eighteen hundredths + 8 thousandths
Eighteen hundredths = 18/100 = 0.18
8 thousandths = 8/1000 = 0.008
0.18 + 0.008 = 0.188
(v) 99 hundredths + 89
99 hundredths = 99/100 = 0.99
Adding the two numbers: 0.99 + 89 = 89.99
Q6:Word Problems
(a) Find the area of a rectangle whose length is 78.73 units and breadth is 45.2 units.
Sol: The formula for area A of a rectangle is A = L × B
Length L = 78.73 units
Breadth B = 45.2 units
Area = 78.73 × 45.2
Calculate: 78.73 × 45.2 = 78.73 × (45 + 0.2) = (78.73 × 45) + (78.73 × 0.2)
78.73 × 45 = 3542.85
78.73 × 0.2 = 15.746
Sum = 3542.85 + 15.746 = 3558.596 square units
Therefore, the area of the rectangle is 3558.596 square units.
(b) Mr. Fred bought 25.60 meters of fabric to tailor window drapes. He bought the fabric on sale for Rs. 5.29 per meter, how much did Mr. Fred spend?
Sol: Total Cost = Length × Cost per metre
Length = 25.60 m
Cost per m = Rs. 5.29
Total = 25.60 × 5.29
25.6 × 5.29 = 25.6 × (5 + 0.29) = 25.6 × 5 + 25.6 × 0.29
25.6 × 5 = 128.0
25.6 × 0.29 = 7.424
Total = 128.0 + 7.424 = Rs. 135.424
Therefore, Mr. Fred spent Rs. 135.424 on the fabric.
(c) Ron purchased a bag for Rs. 134.60, a book for Rs. 328.23 and a tie for Rs. 80.55. How much is left with him if he had Rs. 600 in all?
Sol: Initial amount = Rs. 600
Total cost = 134.60 + 328.23 + 80.55 = 543.38
Money left = 600 - 543.38 = Rs. 56.62
Therefore, Ron has Rs. 56.62 left after the purchases.
(d) There are 80 cookies in a basket. 73 are choco chips cookies and the remaining are basic cookies. What fraction of the cookies are basic? Write your answer in decimal.
Sol: Number of basic cookies = 80 - 73 = 7
Fraction = 7/80
Convert to decimal: 7 ÷ 80 = 0.0875
So, the fraction of basic cookies in decimal form is 0.0875
FAQs on Worksheet Solutions: Decimals
| 1. What are decimals and how are they used in everyday life? |  |
| 2. How do you add and subtract decimals? | |
| 3. What is the difference between a terminating decimal and a repeating decimal? | |
| 4. How can I convert a decimal to a fraction? | |
| 5. Why is it important to understand decimals in mathematics? | |
