Question 13
Write the denominator of rational number 2575000 in the form 2m×5n, where m, n are non - negative integers. Hence, write its decimal expansion, without actual division.
Denominator of the rational 2575000 number is 5000.
Now, factors of 5000
=2×2×2×5×5×5×5=(2)3×(5)4 which is of the type 2m×5n.
Where m = 3 and n = 4 are non - negative integers
∴ 2575000=25723×54×22
= 51424×54=514(10)4
= 51410000=0.0514
Thus, 0.0514 is the required decimal expansion.