Terminating decimals have a limited number of digits after the decimal point.
Example:
5150.21 = 5150 21/100
Recurring decimals have one or more repeating numbers after the decimal point which continue on infinitely.
Example: 6232.3333 = 6232 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: 0.968407803.....
Example: 8369.3 = 8369 3/10
Example: 1399.31 = 1399 31/100
Example: 6509.524 = 6509 524/1000
Example: 40016.2926 = 40016 2926/10000
Decimal to fraction results for: 3.0144 in simple form.
Whole number-integral part: 3
Fractional-decimal part: 0144
3.0144 = 3 0144/10000
a/b = numerator/denominator = 0144/10000
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: 7540.23 = 7540 23/100
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:
8765.6666 = 8765 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: 0.141134472.....