Advertisements
Advertisements
Question
Express the following decimal as a rational number.
4.6724
Advertisements
Solution
Let x = 4.6724
= 4.6724724...
Here, only numbers 724 is being repeated, so first we need to remove 6 which proceeds 724.
We multiply by 10 so that only the recurring digits remain after decimal.
∴ 10x = 46.724724.... ....(1)
The number of digits recurring in equation (1) is 3, so we multiply both sides of the equation (1) by 1000.
∴ 10000x = 1000 x 46.724724...
= 46724.724.... ....(2)
On subtracting (1) from (2), we get
9990x = 4678
∴ x = `(46678)/(9990)`
= `(23339)/(4995)`
∴ 4.6724 = `(763)/(999)`
= `(23339)/(4995)`
APPEARS IN
RELATED QUESTIONS
Classify the decimal form of the given rational number into terminating and non-terminating recurring type.
`13/5`
The number \[\ce{0.\overset{\bullet}{4}}\] in `p/q` form is ______.
Write the numerator of the following rational numbers: 0
Express the following integer as a rational number with denominator 7: 0
Express `3/5` as a rational number with denominator: − 35
State if the following fraction has a terminating decimal.
`(59)/(75)`
State if the following fraction has a terminating decimal.
`(125)/(213)`
Express the following decimal as a rational number.
2.67
Write the following rational number in decimal form.
`7/9`
Write the decimal form of the following rational numbers
`1 2/5`
