# Exercise 1.4 - Chapter 1 Real Numbers class 10 ncert solutions Maths PDF Download [2022-2023]

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Question 1:

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

Answer:

(i)

The denominator is of the form 5m.

Hence, the decimal expansion ofis terminating.

(ii)

The denominator is of the form 2m.

Hence, the decimal expansion of is terminating.

(iii)

455 = 5 × 7 × 13

Since the denominator is not in the form 2m × 5n, and it also contains 7 and 13 as its factors, its decimal expansion will be non-terminating repeating.

(iv)

1600 = 26 × 52

The denominator is of the form 2m × 5n.

Hence, the decimal expansion of  is terminating.

(v)

Since the denominator is not in the form 2m × 5n, and it has 7 as its factor, the decimal expansion of  is non-terminating repeating.

(vi)

The denominator is of the form 2m × 5n.

Hence, the decimal expansion of is terminating.

(vii)

Since the denominator is not of the form 2m × 5n, and it also has 7 as its factor, the decimal expansion of  is non-terminating repeating.

(viii)

The denominator is of the form 5n.

Hence, the decimal expansion of  is terminating.

(ix)

The denominator is of the form 2m × 5n.

Hence, the decimal expansion of  is terminating.

(x)

Since the denominator is not of the form 2m × 5n, and it also has 3 as its factors, the decimal expansion of  is non-terminating repeating.

Question 2:

Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

Answer:

(viii)

Question 3:

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form  , what can you say about the prime factor of q?

(i) 43.123456789 (ii) 0.120120012000120000… (iii)

Answer:

(i) 43.123456789

Since this number has a terminating decimal expansion, it is a rational number of the form and q is of the form

i.e., the prime factors of q will be either 2 or 5 or both.

(ii) 0.120120012000120000 …

The decimal expansion is neither terminating nor recurring. Therefore, the given number is an irrational number.

(iii)

Since the decimal expansion is non-terminating recurring, the given number is a rational number of the form  and q is not of the form  i.e., the prime factors of q will also have a factor other than 2 or 5.

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