0.16 16 Repeating as a Fraction
What is 0.16 16 Repeating?
0.16 16 repeating is a decimal number that has a repeating pattern of 16. This means that the digits "16" will continue to repeat indefinitely. For example, the decimal expansion of 0.16 16 repeating would be:
0.1616161616...
Converting 0.16 16 Repeating to a Fraction
To convert 0.16 16 repeating to a fraction, we can use the following steps:
- Let x = 0.161616...
- Multiply both sides of the equation by 100 to get rid of the decimal point: 100x = 16.161616...
- Subtract the original equation from the new equation: 100x - x = 16.161616... - 0.161616...
- Simplify the equation: 99x = 16
- Divide both sides of the equation by 99: x = 16/99
Therefore, 0.16 16 repeating as a fraction is:
16/99
Properties of 16/99
- Simplified Form: 16/99 is already in its simplest form.
- Equivalent Ratios: 16/99 is equivalent to other ratios such as 32/198, 48/297, and so on.
- Decimal Expansion: The decimal expansion of 16/99 is 0.161616..., which is the repeating decimal we started with.
In conclusion, 0.16 16 repeating can be converted to a fraction, which is 16/99. This fraction has a unique set of properties, including its simplified form, equivalent ratios, and decimal expansion.
