Question

Convert the decimal expansion 0.1777 into a rational number

Answer 1

The rational form of the given number 0.1777 =
`(1777)/(10,000)`

Explanation:

The rational number is expressed as a number on the form of
`((p)/(q) ) , q \\eq 0`

Now,here the given number in decimal form = 0.1777

To remove the decimal, firstly count the number of digits AFTER DECIMAL.

Here, number of digits after decimal = 4

SO, the decimal can be removed and replaced by 1 , by dividing with 1,0000.

`\implies 0.1777  = \frac{01,777} {10,000}  = (1777)/(10,000)`

Hence, the rational form of the given number 0.1777 =
`(1777)/(10,000)`