We have given a number 19/3125 and we have to prove that the given rational number is a terminating decimal and also asked to express in decimal form without actual division.
Kindly solve the above problem in detail
RS Aggarwal, Class 10, Chapter 1C, question no 1(vi)
Here, denominator is 3125=2^5.
The rational number can be written as:
19/3125=19/(2^0×5^5), which is similar to the form of (2^m×5^n) in denominator.
Hence, the given rational is terminating,
and its decimal expansion is 19/3125=0.00608.