How can the number 3.571428 be written as a ratio of two integers?

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caledon's profile pic

caledon | High School Teacher | (Level 3) Senior Educator

Posted on

Decimals can be thought of as the calculated form of a ratio, i.e. a fraction.

For example: .5 is just another way of saying 1:2, or 1/2

Put in mathematical terms: `0.5 = 1/2 `

If we multiply both sides by the fraction's denominator, we get the numerator.

2 x (0.5) = 1

So: Denominator x Decimal form = Numerator

We need to find the Denominator and Numerator; our only clue is that these will be integers.

What we need to do is multiply the decimal by a series of integers that will progressively eliminate the lowest; basically, multiply so that the last number will become a number ending in 0. For example, the last digit in the given decimal is an 8: multiplying 8 by 5 will give us 40, which allows us to get rid of the millionths place and get that much closer to a whole number.

3.571428 x 5 = 17.85714

17.85714 x 5 = 89.2857

89.2857 x 10,000 = 892,857 (the numerator)

5x5x10,000 = 250,000 (the total number we divided by)

So 3.571428 = 892,857 / 250,000

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The easiest way to convert decimal form into ratio is by removing the decimal.

The decimal is removed by cancelling it off from the given number, and then dividing it with the number 1 plus the number of zeroes, one for each number after the decimal in the given number.

Such that when the given number is: 3.571428

We remove the decimal by :

3571428/ 1000,000

Now we simplify it by dividing it and bringing it to the lowest values:

Say, that we divide it by 6, we get:

892,857/250,000, which is therefore the ratio form.

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