The document Ex 1.4 NCERT Solutions - Real Numbers Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.

All you need of Class 10 at this link: Class 10

**Q.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:****(i) 13/3125 ****(ii) 17/8 ****(iii) 64/455 ****(iv) 15/1600****(v) 29/343 ****(vi) 23/(2 ^{3}5^{2}) **

If the denominator has factors other than 2 and 5 then it has a non-terminating decimal expansion.

Factorizing the denominator, we get,

3125 = 5 × 5 × 5 = 5

Since, the denominator has only 5 as its factor, 13/3125 has a terminating decimal expansion.

Factorizing the denominator, we get,

Since, the denominator has only 2 as its factor, 17/8 has a terminating decimal expansion.**(iii) 64/455**

Factorizing the denominator, we get,

455 = 5 × 7 × 13

Since, the denominator is not in the form of 2^{m} × 5^{n}, thus 64/455 has a non-terminating decimal expansion.**(iv) 15/ 1600**

Factorizing the denominator, we get,

1600 = 2^{6}5^{2}

Since, the denominator is in the form of 2^{m} × 5^{n}, thus 15/1600 has a terminating decimal expansion.**(v) 29/343**

Factorizing the denominator, we get,

343 = 7 × 7 × 7 = 7^{3} Since, the denominator is not in the form of 2^{m} × 5^{n} thus 29/343 has a non-terminating decimal expansion.**(vi) 23/(2 ^{3}5^{2})**

Clearly, the denominator is in the form of 2

Hence, 23/ (2

As you can see, the denominator is not in the form of 2

Hence, 129/ (2

6/15 = 2/5

Since, the denominator has only 5 as its factor, thus, 6/15 has a terminating decimal expansion.

35/50 = 7/10

Factorising the denominator, we get,

10 = 2 5

Since, the denominator is in the form of 2

77/210 = (7× 11)/ (30 × 7) = 11/30

Factorising the denominator, we get,

30 = 2 × 3 × 5

As you can see, the denominator is not in the form of 2

13/3125 = 0.00416

**(ii) 17/8**

17/8 = 2.125

**(iii) 64/455** has a Non terminating decimal expansion

**(iv)15/ 1600**

15/1600 = 0.009375

**(v) 29/ 343** has a Non terminating decimal expansion

**(vi)23/ (2 ^{3}5^{2}) = 23/(8×25)= 23/200**

**(vii) 129/ (2 ^{2}5^{7}7^{5}) has a Non terminating decimal expansion **

**(viii) 6/15 = 2/5 **

**(ix) 35/50 = 7/10 ****35/50 = 0.7 **

**(x) 77/210 has a non-terminating decimal expansion. ****Q.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. . .****Solutions:****(i) 43.123456789 **

Since it has a terminating decimal expansion, it is a rational number in the form of p/q and q has factors of 2 and 5 only.

**(ii) 0.120120012000120000. . .**

Since, it has non-terminating and non- repeating decimal expansion, it is an irrational number.

Since it has non-terminating but repeating decimal expansion, it is a rational number in the form of p/q and q has factors other than 2 and 5.

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

51 videos|346 docs|103 tests