Terminating decimals have a limited number of digits after the decimal point.
Example:
8200.71 = 8200 71/100
Recurring decimals have one or more repeating numbers after the decimal point which continue on infinitely.
Example: 7653.3333 = 7653 3333/10000 = 333/1000 = 33/100 = 1/3 (rounded)
Irrational decimals go on forever and never form a repeating pattern. This type of decimal cannot be expressed as a fraction.
Example: 0.281853330.....
Example: 6210.2 = 6210 2/10
Example: 4072.80 = 4072 80/100
Example: 7544.181 = 7544 181/1000
Example: 53747.8240 = 53747 8240/10000
Decimal to fraction results for: 3.0339 in simple form.
Whole number-integral part: 3
Fractional-decimal part: 0339
3.0339 = 3 0339/10000
a/b = numerator/denominator = 0339/10000
Terminating decimals are rather easy to convert. You can manually convert any terminating decimal into a fraction using these steps:
Step 1: Write the decimal number in fraction format, with the number as the numerator and 1 in the denominator.
Step 2: Now, multiply the numerator and the denominator by 10 for every digit left of the decimal point.
Step 3: Next, reduce the fraction into its simplest form.
Terminating Decimal to Fraction Example: 2548.13 = 2548 13/100
Non-terminating decimals are those decimals which have an infinite number of recurring digits. It is a bit tricky to convert non-terminating decimals into fractions. Next we'll explain the steps. For example, let us find the value of 0.4444... in fraction form.
Step 1: Take the repeating decimal you are trying to convert as x. Let x be equal to 0.44444….
Step 2: Multiply the value of X by the power of 10, such that the resulting number has the same number on the right side of the decimal.
Hence, 10x = 4.44444….
Step 3: Subtact the output of step 2 from step 1
10x-x = 4.444444...-0.4444444….
9x= 4
= 4/9
Step 4: Resulting in a fraction number of the decimal number.
x=4/9
Recurring Decimal to Fraction Example:
9886.6666 = 9886 6666/10000 = 666/1000 = 66/100 = 2/3 (rounded)Irrational decimals go on forever and never form a repeating pattern. This type of decimal cannot be expressed as a fraction.
Irrational Decimal Example: 0.416356154.....