Q1 of 124 Page 1

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

(i) (ii)


(iii) (iv)


(v)

(i) 8 = 23 since the denominator is of the form 2m therefore the expression is terminating.


(ii) 441 = 32 × 72 since the denominator is not in the form of 2m and 5n Therefore the given expression is Non-terminating repeating


(iii) =


10 = 2×5 therefore the denominator is of the form 2m × 5n


Hence, the given expression is Terminating


(iv) = =


30 = 2×3×5


Since the denominator is not of the form 2m × 5n


Hence, the given expression is Non-terminating repeating Terminating


(v)


Since the denominator is not in the form 2m × 5n


Hence, the given expression is Non-terminating repeating Terminating


More from this chapter

All 124 →
11

Prove that for any prime positive integer p, is an irrational number.

 12

If p, q are prime positive integers, prove that is an irrational number.

 2

Write down the decimal expansions of the following rational numbers by writing their denominators in the form, where m, n are non-negative integers.

(i) (ii)


(iii) (iv)


(v)

3

What can you say about the prime factorizations of the denominators of the following rational?

(i) 43.123456789


(ii)


(iii)


(iv) 0.120120012000120000…