# PSEB Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4

PSEB Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4

## PSEB 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.4

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 :

Solution:

(i)Let x = 13/3125 ………..(1)

Compare (1) with x = p/q

Here p = 13 and q = 3125

Prime factors of q = 3125 = 5 × 5 × 5 × 5 × 5 = 5^{5} × 2^{0}

which are of the form 2^{n} × 5^{m} here n = 0, m = 5

which are non negative integers.

∴ x = 13/3125 have a terminating decimal expansion.

Question 2.

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

Solution:

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 f, what can you say about the prime factors of q?

(i) 43.123456789

(ii) O.120120012000120000……

(iii) 4.3.123456789

Solution:

(i) Let x= 43.123456789 ……….. (1)

It is clear from the number that x is rational number.

Now remove the decimal from the number

Where p = 43123456789 and q = 10^{9}

Now, Prime factors of q = 10^{0} = (2 × 5)^{9}

⇒ Prime factors of q are 2^{9} × 5^{9}

(ii) Let x = 0.120120012000120000

It is clear from the number that it is an irrational number.

(iii) Let x = 43.123456789 …. (1)

It is clear that the given number is a rational number because it is non-terminating and repeating decimal.

To show that (i) is of the form p/q

Multiply (1) with 10^{9} on both sides,

10^{9} x = 43123456789.123456789 …………….(2)

Subtract (1) from (2), we get:

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