Fractions can be changed to decimals and decimals to fractions in a few simple steps. The rule is that both fractions and decimals are different ways to express the same relationship between numbers, a ratio, using division and multiplication. All fractions can be written as a/b, where the two numbers have a relationship with one another.
The top number(the numerator) is part of the bottom number (the denominator). The words numerator and denominator are just math language for part and whole, or top number and bottom number. To turn the fraction into a decimal, just divide the numerator by the denominator. Thus, 2/5 is the same thing as “2 divided by 5” or 0.4, 1/2 is 1 divided by 2, or 0.5, and 3/4 is 3 divided by 4 or .75.
Some numbers don’t divide as nicely, and they have an interesting pattern of repeating decimals. Therefore , 1/3 is 1 divided by 3, or 0.33, 2/3 is 2 divided by 3 or 0.66, 1/6 is 1 divided by 6 or 0.166, and 5/6 is 5 divided by 6 or 0.833. (Notice I didn’t use 2/6, because that’s the same as 1/3, 3/6 is the same as 1/2, and 4/6 is the same as 2/3.)
Decimals fall into two different groups, terminating and repeating, and there are slightly different steps for turning each type from decimal into fraction. It’s easier to see with an example, using long division. With the fraction 3/8, 3 is divided by 8, or .375, and every remainder gets smaller until the remainder is zero. At that point, the decimal stops repeating. If that last remainder is not zero (as in 5/6), it will eventually repeat itself as in 0.833.
When the decimal doesn’t repeat, it can be expanded and solved into a fraction that way. For example, 0.4 can be expressed as 4/10 divided by 2/2 (to put it in simplified terms ) or 2/5. When the decimal does repeat itself, turn the statement into an equation in order to get rid of the repeating part.
If X = .2222, then 10X =2.222. Then you can subtract the two equations: 10x-x = 2.22-.22, 9x = 2, or x = 2/9. When 2 is divided by 9, the answer is 0.2222; full circle either way.
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