0.08 Recurring as a Fraction
What is 0.08 Recurring?
0.08 recurring, also known as 0.08̄, is a repeating decimal where the sequence of digits "08" repeats indefinitely. This type of decimal is also referred to as a recurring decimal or a non-terminating decimal.
Converting 0.08 Recurring to a Fraction
To convert 0.08 recurring to a fraction, we can use the following steps:
Step 1: Let x = 0.08̄
Step 2: Multiply both sides by 100 to get rid of the decimal point: 100x = 8.08̄
Step 3: Subtract x from both sides to get: 99x = 8
Step 4: Divide both sides by 99 to solve for x: x = 8/99
Result:
0.08 recurring as a fraction is equal to 8/99.
Properties of 0.08 Recurring as a Fraction
- Equivalent Ratios: 8/99 is an equivalent ratio to other fractions, such as 16/198, 24/297, and so on.
- Simplification: 8/99 is already in its simplest form, as the greatest common divisor of 8 and 99 is 1.
- Decimal Equivalent: The decimal equivalent of 8/99 is 0.08̄, which is a recurring decimal.
In conclusion, 0.08 recurring as a fraction is equal to 8/99, which can be used in various mathematical applications and problems.
