Question

without actually performing the long division state whether the following rational numbers is terminating or non terminating and write them in decimal form: (1) 93/420 (2) 14587/1250 (3) 987/10500 (4) 6/1250 Pls guys give correct ans. it's very urgent....I m losing my 15 points so pls...give ans..​

Answer 1

Answer:

(i) Given : 23/8

23/ 2³

Here, the factors of the denominator 8 are 2³ , which is in the form 2ⁿ 5^m .

So , 23/8 has terminating decimal expansion.

23/8 = 23 × 5³ /2³ × 5³ = 23 × 125 / (2×5)³

= 2875/10³ = 2875/1000 = 2.875

Hence, the decimal expansion of 23/8 is 2.875.

(ii) Given : 125/441

125 / 3² x 7²

Here, the factors of the denominator 441 are 3² × 7², which is not in the form 2ⁿ 5^m .

So , 125/441 has a non-terminating repeating decimal expansion.