Students can Download Class 10 Maths Chapter 8 Real Numbers Ex 8.4 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 10 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

## Karnataka State Syllabus Class 10 Maths Chapter 8 Real Numbers Ex 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:

Answer:

(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 a non-terminating repeating expansion.

Question 2.

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

Answer:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

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) \(43 . \overline{123456789}\)

Answer:

(i) 43.123456789

\(\frac{p}{q}\) is a rational number

Prime factor of q:

q = 10^{9 }= 2^{9} × 5^{9}

(ii) 0.120120012000120000…………

This is an irrational number

(iii) \(43 . \overline{123456789}\)

This is a rational number.

Because Prime factors of ‘q’ are continued in non-terminating decimal expansion.