Question

write decimal expantion for 7/8 without actual division​

Answer 1

Answer:

0.875

Step-by-step explanation:

To find the decimal expansion of 7/8 without actual division, first factorise the denominator in its prime factors

\begin{gathered}\frac{7}{8} \\ \\ = \frac{7}{ {2}^{3} } \\\end{gathered}

8

7

=

2

3

7

multiply and divide by 5 cube

\begin{gathered}\frac{7 \times {5}^{3} }{ {2}^{3} \times {5}^{3} } \\ \\ = \frac{7 \times 125}{ {(2 \times 5)}^{3} } \\ \\ = \frac{875}{ {(10)}^{3} } \\ \\ = \frac{875}{1000} \\ \\ = 0.875 \\ \\ so \\ \\ \frac{7}{8} = 0.875 \\ \\\end{gathered}

2

3

×5

3

7×5

3

=

(2×5)

3

7×125

=

(10)

3

875

=

1000

875

=0.875

so

8

7

=0.875

Answer 2

Answer:

0.875

Step-by-step explanation:

7/2^3= 7/2^3*5^0  so,7/8     has a terminating decimal expansion