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# Worksheet on Decimal Fractions

## Worksheet of Decimal Fractions

### Solved Questions on Decimal Fractions

1. Convert the non-terminating decimal 0.666... to a fraction.

a) 2 / 3
b) 4 / 3
c) 6 / 5
d) 7 / 9

Explanation: Let, x = 0.666... --------- (1)
Multiplying 10 on both the sides we get,
10x = 6.666… ----------------- (2)

Subtracting the two equations,
10x - x = 6.666 - 0.666
9x = 6
x = 6/9 or 2/3

Thus, on converting the non-terminating decimal 0.666... to a fraction we get the result as 2/3.

2. Convert the following:

i) Convert 4 ½ into a decimal fraction.

ii) Convert 6.34 into a decimal fraction.

iii) Convert 8/5 into a decimal fraction.

a) i) 45/10, ii) 634/10, iii) 15/10
b) i) 45/10, ii) 634/100, iii) 15/10
c) i) 45/10, ii) 634/100, iii) 16/10
d) i) 52/10, ii) 634/10, iii) 16/10

Answer: c) i) 45/10, ii) 634/100, iii) 16/10

Explanation: i) 4 ½ can be written as 4.5 and since there is only one place after the decimal point, its decimal fraction would be 45/10.

ii) Since there are two places after the decimal point, the decimal fraction of 6.34 would be 634/100.

iii) Multiplying the numerator and the denominator by 2 we get, 8/5 = 16/10

3. Kathy purchased 100 Kiwi fruits from a local fruit dealer, only to discover that five of them were rotting. Calculate the decimals of the rotten Kiwi fruits in relation to the total Kiwi fruits purchased by Kathy.

a) 0.02
b) 0.05
c) 0.5
d) 0.07

Explanation: Out of 100 Kiwi fruits, we have 5 rotten ones.
As a result, the percentage of rotten Kiwi fruits is 5/100.
By dividing the numerator 5 by the denominator 100 we get 0.05.

Therefore, the rotten Kiwi fruits are 0.05 in Decimals.

4. Sia bought 12 bags of wheat flour each weighing 4563/100 kg. What will be the total weight in mg?

a) 5475600 mg
b) 564760000 mg
c) 547560000 mg
d) 574560000 mg

Explanation: Total no. of bags = 12
Weight of each bag = 4563/100 kg = 45.63 kg
Total weight = 45.63 x 12 = 547.56 kg
We know that 1 kg = 1000000 mg

Therefore, Total weight = 547.56 x 1000000 = 547560000 mg

5. Find the product of the decimal fractions 15/10 and 45/100.

a) 625/1000
b) 675/1000
c)675/100
d)625/100

Explanation: (15/10) × (45/100) = (15 × 45)/(10 × 100)
(15/10) × (45/100) = 675/1000

Hence, the product of 15/10 and 45/100 is 675/1000.

### Practice Questions on Decimal Fractions

1. Divide the decimal fraction 25/10 by 15/100.

a) 23/2
b) 50/3
c) 53/7
d) 67/2

2. Add the following decimal fractions: (35/10) + (12/100).

a) 47/100
b) 123/100
c) 362/100
d) 423/100

3. Ashley was making shapes out of cardboard, she has made a circle with a circumference of it is 16.09 cm. What will be its diameter (π = 3.14)?

a) 12.5 cm
b) 9.5 cm
c) 5.12 cm
d) 2.3 cm

4. Tim is a postman that works at a local post office. The basic postage is \$1.25 and covers any letter that is lighter than 7.5 grams. For heavier letters, extra postage of \$0.87 is needed for every 10 grams over 7.5 grams. What is the postage needed for a letter that is 37.5 grams?

a) \$4.76
b) \$3.86
c) \$2.32
d) \$12.2

5. Farmer Alex lives 0.35 km away from the farm. His co-worker Jordan lives 39/100 km away from the same farm. Whose house is farther from the farm? By what distance?

a) Jordan lives 0.04 km farther from the farm than Alex.
b) Jordan lives 0.14 km farther from the farm than Alex.
c) Jordan lives 0.014 km farther from the farm than Alex.
d) Jordan lives 0.004 km farther from the farm than Alex.

Answer: a) Jordan lives 0.04 km farther from the farm than Alex.

6. The bill for a pizza was \$14.50. Charles paid for 3/5 of the bill. How much did he pay?

a) \$2.4
b) \$3.2
c) \$5.7
d) \$8.7

7. Jennie bought 6.5 kg of sugar. She used 3750 grams. How many kilograms of sugar were left?

a) 2.75 kg
b) 3.2 kg
c) 4.65 kg
d) 7.8 kg

8. A water pitcher weighs 0.64 kg when empty and 1.728 kg when filled with water. How much does the water weigh?

a) 1.022
b) 1.008
c) 1.088
d) 1.094

9. A cyclist has traveled 145.8 km in the first stage of a race, 136.65 km in the second stage and 162.62 km in the third. How many kilometers must the cyclist still complete if the entire race is 1000 km in length?

a) 554.93 km
b) 598.32 km
c) 600.33 km
d) 613.24 km

10. There are 240 boxes with 25 bags of coffee each. If each bag weighs 0.62 kg, what is the total weight of all the coffee?

a) 3737.00 kg
b) 3720.00 kg
c) 3868.00 kg
d) 3947.00 kg