How do you put 0.051 into a fraction in simplest form?

Answer 1

Step 1)

Remove any decimals in either the numerator or denominator or both by multiplying both the numerator and the denominator by 10 raised to the appropriate power.

example: 0.045/0.16...

Here you see that both the numerator and denominator have decimal numbers. In order to remove the decimal places, the numerator must be multiplied by 1000 (10^3) and the denominator by 100 (10^2). But if we multiply the numerator and the denominator by different numbers the fraction will change (1000/100=10). So always use the largest power of 10 required to remove the decimal. In this example, we have to multiply the fraction by 1000/1000 (=1).

Step 2)

Once the decimal places are removed, try to list out any common factors for the number in the numerator and the number in the denominator.

example: the fraction above is converted to 45/160 after multiplying by 1000/1000.

45=3x3x5

160=2x2x2x2x2x5

As can be seen, the only common factor is 5.

Note: List out only the prime factors.

Step 3)

Divide both the numerator and the denominator by the common factor.

example: dividing 45 by 5 we get 9

dividing 160 by 5 we get 32

Step4)

What ever remains after the numerator and denominator have been divided by the common factors is the reduced form of the fraction.

example: 0.045/0.16 = 9/32

EXAMPLE IN QUESTION:

0.051 (or any other number) can be expressed as 0.051 (or any other number )/1. That is because, anything divided by 1 is itself.

Once 0.051 is expressed as 0.051/1 the above procedure can be followed as below:

(0.051/1) x (1000/1000) = 51/1000

51=17x3

1000=2x2x2x5x5x5

There are no common factors.

Hence the reduced form is 51/1000.