# KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4

KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 are part of KSEEB SSLC Class 10 Maths Solutions. Here we have given Karnataka SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Exercise 8.4.

## Karnataka SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Exercise 8.4

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)

∴ This is terminating decimal expansion.

(ii)

∴ This is terminating decimal expansion.

(iii)
$$\frac{64}{455}=\frac{2^{6}}{5 \times 7 \times 13}$$
∴ This is non-terminating repeating expansion.

(iv)

∴ This is terminating decimal expansion.

(v)
$$\frac{29}{343}=\frac{29}{7^{3}}$$
∴ This is non-terminating repeating expansion.

(vi)

∴ This is terminating decimal expansion.

(vii)
$$\frac{129}{2^{2} 5^{7} 7^{5}}$$
∴ This is non-terminating repeating expansion.

(viii)

∴ This is terminating decimal expansion.

(ix)

∴ This is terminating decimal expansion.

(x)

∴ This is non-terminating repeating 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 $$\frac{p}{q}$$, what can you say about the prime factors of q?
(i) 43.123456789
(ii) 0.120120012000120000….
(iii) $$43 . \overline{123456789}$$
Solution:
(i) 43.123456789
∴ The given decimal expansion terminates.
∴ It is rational of the form $$\frac{p}{q}$$

Hence, p = 43123456789 and q = 29 × 59
Prime factors of q are 29 and 59.

(ii) 0.120120012000120000…
∵ The given decimal expansion is neither terminating nor repeating.
∴ It is irrational number, hence cannot be written in p/q form.

(iii) $$43 . \overline{123456789}$$
∵ The given decimal expansion is non-terminating repeating.
∴ It is rational number.

Multiplying both sides by 1000000000, we have
1OOOOOOOOOx = 43123456789.123456789…
… (2)
Subtracting (1) from (2), we have
(1000000000x) – x
= (43123456789.123456789 ) – 43.123456789…
⇒ 999999999x = 43123456746

Here, p = 4791495194 and q = 111111111, which is not of the form 2m × 5n i.e., the prime factors of q are not of the form 2m × 5n.

We hope the given KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 will help you. If you have any query regarding Karnataka SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Exercise 8.4, drop a comment below and we will get back to you at the earliest.