There is two ways to convert a decimal number into a fraction.
First Way
Example 1
Lets say you have a decimal number 0.23
To change the decimal number 0.23 into a fraction
!. Write the decimal with the number 1 underneath to form a fraction. 0.23/1
2. Multiply the top and button by 100. 23/100
3. Simplify the fraction. 23/100
Example 2
Lets say you have a decimal number 0.802
To change the decimal number 0.802 into a fraction
1. Write the decimal with the number 1 underneath to form a fraction. 0.802/1
2. Multiply the top and bottom by 1000. 802/1000
3. Simplify the fraction. 401/500
Notice that between the two examples, steps one and three are the same; however, sttep two is a little different. The reason for that depeds on how mnay digets are in the decimal number. If there is one digit in the decimal number, multiply both top and bottom numbers by 10, if there are two digits in the decimal number, multiply both top and bottom numbers by 100, if thre are three digits in the decimal number, multiply both top; and bottom numbers by 1000, and so on.
Second Way
Example 1
Lets say you have a decimal number 0.3333333333333333333...
1. Put the decimal into algebraic terms. Let x = 0.3333333333333333333...
2.Move the decimal so the first recurring number is before the decimal point. In this case that means that you need to multiply both sides by 10. 10x = 3.333333333333333333...
3.Remove the decimal numbers by subtracting x from 10x. 9x = 3
4. Solve for x. x = 3/9
5. Simplify the fraction. 1/3
Example 2
Lets say you have a decimal number 0.1231212121212121...
1. Put the decimal into algebraic terms. Let x = 0.1231212121212121...
2.Move the decimal so the first recurring number is before the decimal point. In this case that means that you need to multiply both sides by 100000. 100000x = 12312.12121212121...
3.Remove the decimal numbers by subtracting x from 100000x. 99999x = 12312
4. Solve for x. x = 12312/99999
5. Simplify the fraction. 1368/11111
Notice that the first way are for decimal numbers where the decimal number does not repeat forever and the second way are for decimal numbers that do repeat forever.
The only decimal numbers that you cannot put into a fraction are decimal numbers that go on forever but do not repeat. An example of a number that goes one forever but does not reopeat is $${\mathtt{\pi}}$$. No fraction will equal $${\mathtt{\pi}}$$.
There is two ways to convert a decimal number into a fraction.
First Way
Example 1
Lets say you have a decimal number 0.23
To change the decimal number 0.23 into a fraction
!. Write the decimal with the number 1 underneath to form a fraction. 0.23/1
2. Multiply the top and button by 100. 23/100
3. Simplify the fraction. 23/100
Example 2
Lets say you have a decimal number 0.802
To change the decimal number 0.802 into a fraction
1. Write the decimal with the number 1 underneath to form a fraction. 0.802/1
2. Multiply the top and bottom by 1000. 802/1000
3. Simplify the fraction. 401/500
Notice that between the two examples, steps one and three are the same; however, sttep two is a little different. The reason for that depeds on how mnay digets are in the decimal number. If there is one digit in the decimal number, multiply both top and bottom numbers by 10, if there are two digits in the decimal number, multiply both top and bottom numbers by 100, if thre are three digits in the decimal number, multiply both top; and bottom numbers by 1000, and so on.
Second Way
Example 1
Lets say you have a decimal number 0.3333333333333333333...
1. Put the decimal into algebraic terms. Let x = 0.3333333333333333333...
2.Move the decimal so the first recurring number is before the decimal point. In this case that means that you need to multiply both sides by 10. 10x = 3.333333333333333333...
3.Remove the decimal numbers by subtracting x from 10x. 9x = 3
4. Solve for x. x = 3/9
5. Simplify the fraction. 1/3
Example 2
Lets say you have a decimal number 0.1231212121212121...
1. Put the decimal into algebraic terms. Let x = 0.1231212121212121...
2.Move the decimal so the first recurring number is before the decimal point. In this case that means that you need to multiply both sides by 100000. 100000x = 12312.12121212121...
3.Remove the decimal numbers by subtracting x from 100000x. 99999x = 12312
4. Solve for x. x = 12312/99999
5. Simplify the fraction. 1368/11111
Notice that the first way are for decimal numbers where the decimal number does not repeat forever and the second way are for decimal numbers that do repeat forever.
The only decimal numbers that you cannot put into a fraction are decimal numbers that go on forever but do not repeat. An example of a number that goes one forever but does not reopeat is $${\mathtt{\pi}}$$. No fraction will equal $${\mathtt{\pi}}$$.
