Question

Convert 4.567878...into rational number​

Answer 1

Answer:

The conversion of the given decimal number into rational fraction can be carried out by using following conversion steps: Step I: Let x = 4.567878… Step II: After examining we find that the repeating digits are '78'. Step III: Now we place the repeating digits '78' to the left of decimal point.

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Answer 2

Answer:

step1

let x=4.567878

step2

78 is repeating

step3

now place the repeating digit78 to left decimal point.

10,000=45678.787878

step4

now we need to replace the tepeating digit to left decimals point in the original decimal point.to do so we need to shift the decimal point to the right by 4 places.this can be done by multiplying given number by 10,000.

100x=456.787878

step4

now we ha e to subtract both the left and write hand sides of equation.

10,000-1000x=45678.787878-456.787878

=9,900x=45,222

=x=45222÷9,900

the rational fraction can be further reduced to

=x=7537÷1650(divide both numinator and denominator by 6)

so,the national convertion of the given decimal

number is 7537

upon

1650