Decimal Fractions Questions

Decimal fractions questions are offered here to help students comprehend the concept and achieve high results on their final exams. As each question comes with a detailed explanation, students can use these questions to improve their grades. We have also offered practice problems for pupils to help them develop their problem-solving skills. Click here for more information on decimal fractions.

Decimal Fractions Questions with Solutions

1. Find the decimal fractions among the given options:

7/6, 20/40, 144/100, 26/10, 25/30.

Solution:

A fraction whose denominator is the power of 10, such as 10¹, 10², 10³, etc is called the decimal fraction.

Among the given options, 7/6, 20/40, and 25/30 are not decimal fractions, because the denominator of these fractions is not the powers of 10.

Whereas, 144/100 and 26/10 are decimal fractions, whose denominator is the power of 10.

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

Solution: 362/100.

Given decimal fractions: (35/10) +(12/100).

As the denominators of the decimal fractions are different, take the LCM of 10 and 100.

Thus, the LCM of 10 and 100 is 100.

To make the denominator of the decimal fractions same, multiply the numerator and denominator of the decimal fraction by 10.

(35/10) + (12/100) = [(35×10) /(10×10)] + (12/100)

So, (35/10) + (12/100) = (350 + 12)/100

(35/10) + (12/100) = 362/100

Therefore, the sum of the decimal fractions (35/10) and (12/100) is 362/100.

3. How to convert the fraction 1/8 into a decimal fraction.

Solution:

To convert the fraction 1/8 into a decimal fraction, follow the steps given below:

Step 1: Check the denominator of the given fraction. If it can be written in the prime factorization of either 2 or 5, it can be easily converted into a decimal fraction. So, in the given fraction, 8 is the denominator, whose prime factorization is 2 × 2 × 2.

Step 2: As 10 and 100 are not multiples of 8, we will check with the next power of 10, which is 1000.

Step 3: Now, check whether 1000 is a multiple of 8. And we found that 1000 is the multiple of 8.

Step 4: Now, multiply the numerator and denominator of 1/8 by 125, and we get the decimal fraction.

I.e. 1/8 = (1×125) / (8×125) = 125/ 1000.

Thus, the decimal fraction of 1/8 is 125/1000.

4. Which among the following is a decimal fraction: 5/15, 2/10, 7/20, 65/100.

Solution:

We know that decimal fractions are fractions, such that the denominator of the fraction should be the powers of 10, such as 10, 100, 1000, and so on.

In the fractions 5/15 and 7/20, the denominator is not a power of 10. Hence, 5/15 and 7/20 are not decimal fractions.

Whereas in the fractions 2/10 and 65/100, the denominators are the powers of 10, such as 10¹ and 10², respectively.

Hence, among the given fractions 2/10 and 65/100 are the decimal fractions.

5. What is the sum of the decimal fractions 25/100 and 30/100?

Solution:

Given decimal fractions: 25/100 and 30/100.

As the denominators are the same in both decimal fractions, we can directly add the numerators.

Thus,

(25/100) + (30/100) = (25 + 30)/100

(25/100) + (30/100) = 55/100.

Hence, the sum of the decimal fractions 25/100 and 30/100 is 55/100.

6. Subtract the decimal fraction 21/100 from 50/100.

Solution:

To find: (50/100) – (21/100)

As the denominator of both decimal fractions is the same, we can directly subtract the numerator values.

(50/100) – (21/100) = (50 – 21)/100

(50/100) – (21/100) = 29/100.

Therefore, subtraction of 21/100 from 50/100 gives 29/100.

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

Solution:

Like multiplying fractions, we can also perform multiplying decimal fractions.

To find the product of decimal fractions, multiply the numerator of the first decimal fraction with the numerator of the second decimal fraction, and multiply the denominator of the first decimal fraction with the denominator of the second decimal fraction.

It means,

(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.

8. Subtract: 51/100 – 23/10.

Solution:

Given: 51/100 – 23/10

Since the denominators of the decimal fractions are different, take the LCM of 100 and 10 is 100.

Thus, the expression 51/100 – 23/10 can also be written as:

(51/100) – (23/10) = (51/100) – [(23×10) / (10×10)]

(51/100) – (23/10) = (51/100) – (230/100)

Now, the denominators of both the decimal fractions are the same, subtract the numerators.

(51/100) – (23/10) = (51 – 230) / 100

(51/100) – (23/10) = -179/100

Hence, (51/100) – (23/10) is -179/100.

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

Solution:

Given: (25/10) ÷ (15/100)

To divide these decimal fractions, follow the below steps:

Step 1: Take the reciprocal of the second decimal fraction.

I.e., 15/100 becomes 100/15.

Step 2: Now, multiply the first decimal fraction with the reciprocal of the second decimal fraction, to get the answer.

I.e., (25/10) ÷ (15/100) = (25/10) × (100/15)

(25/10) ÷ (15/100) = (25 × 100) ÷ (10 × 15)

(25/10) ÷ (15/100) = 250/15

(25/10) ÷ (15/100) = 50/3

Therefore, the division of 25/10 by 15/100 gives 50/3.

10. Write the decimal fractions for the decimal number 0.6.

Solution:

Given: Decimal number: 0.6.

To convert the given decimal number into the decimal fraction, multiply and divide the decimal number by the powers of 10.

For example, (0.6 × 10)/10 = 6/10

Similarly, (0.6 × 100)/100 = 60/100

(0.6 × 1000)/1000 = 600/1000, and so on.

Therefore, the decimal fractions of 0.6 are 6/10, 60/100, 600/1000, etc.

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Practice Questions

Answer the following question:

1. Give the equivalent decimal fractions for the decimal number 0.05.
2. Find the sum of the decimal fractions 27/10 and 49/100.
3. Divide the decimal fractions: (56/100) ÷ (24/10).

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