Question

write the decimal expansion of 3 / 8 without actual division

Answer 1

Here issss thee answer

Answer 2

The decimal expansion of 3 / 8 without actual division is 0.375.

Given:

Fraction 3/8

To Find:

The decimal expansion of 3 / 8 without actual division

Solution:

To find the decimal expansion without actual division we have to find a constant K, when multiplying the constant K with the numerator and denominator it should make the denominator in terms of 10's power.

$\frac{3}{8} = \frac{3}{2^{3} }$

If we multiply the numerator and denominator by 5³, we will get the denominator as 10³=1000

$\frac{3}{2^{3} } * \frac{5^{3}}{5^{3} } \\\\= \frac{3*5^{3}}{2^{3}*5^{3}}$

$=\frac{3*125}{8*125} \\\\=\frac{375}{1000}$

Since the denominator has 3 zeroes we have to place the decimal before the three digits of the numerator number.

= 0.375

The decimal expansion of 3 / 8 without actual division is 0.375.

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