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 :
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 1
Solution:
(i)
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 2
∴ This is terminating decimal expansion.

(ii)
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 3
∴ This is terminating decimal expansion.

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

(iv)
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 4
∴ This is terminating decimal expansion.

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

(vi)
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 5
∴ This is terminating decimal expansion.

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

(viii)
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 6
∴ This is terminating decimal expansion.

(ix)
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 7
∴ This is terminating decimal expansion.

(x)
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 8
∴ This is non-terminating repeating expansion.

KSEEB Solutions

Question 2.
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
Solution:
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 9
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 10
KSEEB SSLC Class 10 Maths Solutions Chapter 8 Real Numbers Ex 8.4 11

KSEEB Solutions

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 \(\frac{p}{q}\)
MP Board Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 7
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.
MP Board Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 8
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
MP Board Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 9
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.

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