# Write the following in decimal form and say what kind of decimal expansion each has: i) 36/100 ii) 1/11 iii) \(4{\Large\frac{1}{8}}\) iv) 3/13 v) 2/11 vi) 329/400

**Solution:**

i) 36/100

36/100 = 0.36

Thus, 36/100 in decimal format is represented as 0.36.

This is a terminating decimal number.

ii) 1/11

The remainder 1 keeps repeating. So, 1/11 = 0.0909... and it can be written as 1/11 = 0.09

This is a non-terminating recurring decimal.

iii) \(4{\Large\frac{1}{8}}\)

\(4{\Large\frac{1}{8}}\) can be expressed as 33/8 in terms of improper fraction.

Thus, \(4{\Large\frac{1}{8}}\) = 33/8 = 4.125

Thus, \(4{\Large\frac{1}{8}}\) in decimal form is written as 4.125.

This is a terminating decimal number because the remainder is zero.

iv) 3/13

Thus, 3/13 = 0.23076923...

We see that the set of numbers 230769 after the decimal point keeps repeating. So, this is a non-terminating recurring decimal.

v) 2/11

Thus, 2/11 = 0.1818

Here, we see that the block of numbers 18 keeps repeating. Hence, this is a non-terminating recurring decimal.

vi) 329/400

329/400 = 329 ÷ (4 × 100) = 0.8225

Now, 82.25/100 = 0.8225

Thus, 329/400 in decimal form is written as 0.8225.

This is a terminating decimal number because the remainder is zero.

**ā Check: **NCERT Solutions for Class 9 Maths Chapter 1

**Video Solution:**

## Write the following in decimal form and say what kind of decimal expansion each has: i) 36/100 ii) 1/11 iii) \(4{\Large\frac{1}{8}}\) iv) 3/13 v) 2/11 vi) 329/400

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.3 Question 1

**Summary:**

We see that in decimal form 36/100, \(4{\Large\frac{1}{8}}\), 329/400 are terminating decimals, whereas 1/11, 3/13, 2/11 are non-terminating recurring decimal.

**ā Related Questions:**

- You know that 1/7 = 0.142587. Can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how?
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- Express 0.99999 .... in the form of p/q. Are you surprised with your answer? With your teacher and classmates discuss why the answer makes sense?
- What can be the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

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