Question

After how many places the decimal form of 125÷2^4×5^3 will terminate ​

Answer 1

125÷2^4×5^3

5^3÷2^4×5^3

5^3÷4^3×5^3

( 5÷4×5)^3

(6.25)^3

244.140625

the decimal will terminate up to 6 decimal spaces

Answer 2

Answer:

After four places the decimal form of  $\frac{125}{2^4\times5^3}$ will terminate.

Step-by-step explanation:

Given,   $\frac{125}{2^4\times5^3}$....(1)

Now we try to expand equation (1)

considering the decimal part

${2^4\times5^3} =$ (2 × 2 × 2 × 2) × (5 × 5 × 5)

⇒ ${2^4\times5^3} =$ (16) × (125)

⇒ ${2^4\times5^3} =$ 2000

Hence the value in the denominator is 2000.

Now we try to solve numerator and denominator.

i.e.   $\frac{125}{2000}$.

= 0.0625

And as we can count there are four numbers after the decimal (0, 6, 2, 5)

Therefore, after four places the decimal form of  $\frac{125}{2^4\times5^3}$ will terminate.

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