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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

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

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.

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

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

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

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

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

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

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

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.

☛ 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.

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