Question

write the decimal expansion of 27 over 1250 without actual division

Answer 1

27/1250 =
$27 \div {5}^{3} \times 10 =$
${2}^{3} \times 27 \div {2}^{3 } \times {5}^{3} \times 10 =$
$8 \times 27 \div (2 \times {5}^{3} ) \times 10 =$
$216 \div {10}^{4} =$


$216 \div {10}^{3} \times 10 =$

0.0216

Answer 2

27/1250=27/2×5^4

27×5^4=27×2^3/2×2^3×5^4

216/2^4×5^4

denominator=q is in the form of 2^n×5^m

216/10^4=0.0216 is a terminating decimal

hope it will help you....!