Question

4.567878 convert in to rational numbers
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Answer 1

Step-by-step explanation:

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.

Answer 2

The rational equivalent is 7537/1650

GIVEN

Recurring decimal number = 4.567878.

TO FIND

The rational number of the given recurring decimal.

SOLUTION

We can simply solve the above problem as follows;

We are given a recurring decimal number, 4.567878

Let the rational equivalent of the given number is x.

Let, x = 4.567878 (Equation 1)

Multiplying the whole equation by 100

100x = 456.7878 (Equation 2)

We can observe the that the recurring digits are 78. To bring the recurring on the left side, We will multiply equation 1 by 10000.

10000x = 4567878.78 (Equation 3)

Subtract Equation 2 by Equation 3.

10000x - 100x = 4567878.78 - 456.7878

9900x = 45222

x = 45222/9900

Simplifying further;

x = 7537/1650

Hence, The rational equivalent is 7537/1650

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