Question

Let x =6/1250 be a rational number. Then x has decimal expansion which terminates.

Answer 1

Let x =6/1250 be a rational number. Then x has decimal expansion which terminates after 4 places of decimal

Step-by-step explanation:

$x=\frac{6}{1250}$

$\implies x=\frac{6}{125\times 10}$

$\implies x=\frac{6}{5^3\times 10}$

$\implies x=\frac{6}{5^3\times 10}\times\frac{2^3}{2^3}$ (multiplying numerator and denominator by 2³)

$\implies x=\frac{6\times 2^3}{(5\times 2)^3\times 10}$

$\implies x=\frac{48}{10^4}$

$\implies x=0.0048$

Thus, the decimal expansion of x terminates after 4 places of decimal

Hope this answer is helpful.

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Answer 2

Step-by-step explanation:

Given Let x = 6/1250 be a rational number. Then x has decimal expansion which terminates.

• Given x = 6/1250
• We can write 1250 as 2 x 5^4
• So it will be x = 6 / 2 x 5^4
• Multiply both numerator and denominator by 2^3
• So we get x = 6 x 2^3 / 2^4 x 5^4
• We can write this as
• So x = 6 x 2^3 / (2 x 5)^4
• So we get x = 6 x 8 / 10000
• Or x = 48 / 10000
• Or x = 0.0048

Therefore the decimal places will terminate after 4 decimal places.

Reference link will be

https://brainly.in/question/2103900