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
$$\frac{p}{q}$$ is a rational number
Prime factor of q:
q = 109 = 29 × 59

(ii) 0.120120012000120000…………
This is an irrational number

(iii) $$43 . \overline{123456789}$$
This is a rational number.
Because, Prime factors of ‘q’ are contrinued in non-terminating decimal expansion.

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