In this article, we will share MP Board Class 10th Maths Book Solutions Chapter 1 Real Numbers Ex 1.4 Pdf, These solutions are solved subject experts.

## MP Board Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4

**Question 1.**

Without actually performing the long divison, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

**Solution:**

**MP Board Class 10th Maths Solutions**

Question 2.

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

Solutions:

Multiplying and dividing by 2^{5}, we have

**MP Board Class 10th Maths 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 p/q, what can you say about the prime factors of q?

(i) 43.123456789

(ii) 0.120120012000120000….

(iii) 43.123456789¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

**Solution:**

(i) 43.123456789

∴ The given decimal expansion terminates.

∴ It is rational of the form 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) 43.123456789¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∵ 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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