Question

2. Without actual division, determine which of the following rational numbers have a
terminating decimal representation and which have a non-terminating decimal
representation.
11/ 4
Explain the formula . 2^n , 5^m​

Answer 1

Answer:

the formula 2 and 5 m 60 word /op 9

Answer 2

Step-by-step explanation:

We know that qp is terminating if p and q are co-prime and q is of the form 2m5n; where m and n are non-negative integers.

(A) 253:

Checking co-prime-

Since 3 and 25 have no common factors, hence 3 and 25 are co-prime.

Now,

25=5×5=52

∴ Denominator=52=1×52=20×52

∴ Denominator is of the form 2m5n, where m = 0 and n = 2.

Hence, 253 is a terminating decimal.

(B) 1811:

Checking co-prime-

Since 11 and 18 have no common factors, hence 11 and 18 are co-prime.

Now,

18=2×3×3=2×32

∴ Denominator is not of the form 2m5n.

Hence, 1811 is not a terminating decimal.

(C) 2013:

Checking co-prime-

Since 13 and 20 have no common factors, hence 13 and 20 are co-prime.

Now,

20=2×2×5=22×5

∴ Denominator=22×5=22×51

∴ Denominator is of the form 2m5n, where m = 2 and n = 1.

Hence, 20

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