Terminating decimals have a limited number of digits after the decimal point.
Example:
452.92 = 452 92/100
Recurring decimals have one or more repeating numbers after the decimal point which continue on infinitely.
Example: 7731.3333 = 7731 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: 0.977427932.....
Example: 3945.2 = 3945 2/10
Example: 8583.14 = 8583 14/100
Example: 5461.760 = 5461 760/1000
Example: 20293.2832 = 20293 2832/10000
Decimal to fraction results for: 0.7822 in simple form.
Whole number-integral part: empty
Fractional-decimal part: 7822
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: 3646.85 = 3646 85/100
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:
888.6666 = 888 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: 0.970485074.....
0.7822 = 0 7822/10000
a/b = numerator/denominator = 7822/10000
Use the level of precision to break 0.7822 down further as a fraction. For example 0.7822 with a precision point of 2 equals:
78/100Pie chart representation of the fractional part of decimal 0.7822