**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 = 2^{9} × 5^{9}

Prime factors of q are 2^{9} and 5^{9}.

(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 2^{m} × 5^{n} i.e., the prime factors of q are not of the form 2^{m} × 5^{n}.

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