Question

the decimal expansion of rational number 53/2^4×5^3 will terminate after how many decimal places.

Answer 1

Answer:

Given fraction terminates after 4 decimal places .

Step-by-step explanation:

$Given \: fraction \:\frac{53}{2^{4}\times 5^{3}}$

/* Multiply numerator and denominator by 5, we get

$= \frac{53\times 5}{2^{4}\times 5^{3}\times 5}$

$= \frac{265}{2^{4}\times 5^{4}}$

$= \frac{265}{\left(2\times 5\right)^{4}}$

$=\frac{265}{(10)^{4}}$

$=\frac{265}{10000}$

$=0.0265$

Therefore,

Given fraction terminates after 4 decimal places .

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Answer 2

Answer:

Given fraction terminates after 4 decimal places .

Step-by-step explanation:

Given \: fraction \:\frac{53}{2^{4}\times 5^{3}}Givenfraction

2

4

×5

3

53

/* Multiply numerator and denominator by 5, we get

= \frac{53\times 5}{2^{4}\times 5^{3}\times 5}=

2

4

×5

3

×5

53×5

= \frac{265}{2^{4}\times 5^{4}}=

2

4

×5

4

265

= \frac{265}{\left(2\times 5\right)^{4}}=

(2×5)

4

265

=\frac{265}{(10)^{4}}=

(10)

4

265

=\frac{265}{10000}=

10000

265

=0.0265=0.0265

Therefore,