How do you write 160% as a fraction, mixed number, or whole number in simplest form?
The Correct Answer and Explanation is:
To convert 160% into a fraction, mixed number, or whole number in simplest form, follow these steps:
- Understand the Percent: The term “percent” means “per hundred.” Therefore, 160% can be written as a fraction over 100:
[
160\% = \frac{160}{100}
] - Simplify the Fraction: To simplify the fraction, find the greatest common divisor (GCD) of the numerator (160) and the denominator (100). The GCD of 160 and 100 is 20.
- Divide Both Numerator and Denominator: Divide both the numerator and the denominator by their GCD:
[
\frac{160 \div 20}{100 \div 20} = \frac{8}{5}
]
Now, (\frac{8}{5}) is the fraction representation of 160% in its simplest form. - Convert to Mixed Number: To express (\frac{8}{5}) as a mixed number, divide the numerator by the denominator:
- 8 divided by 5 is 1 with a remainder of 3. Thus, it can be written as:
[
1 \frac{3}{5}
]
Therefore, as a mixed number, 160% is equivalent to (1 \frac{3}{5}).
- Convert to a Whole Number: In terms of whole numbers, 160% indicates that something is 160 parts of a total of 100 parts. In simpler terms, this means it is greater than a whole unit (1). In this case, 160% represents 1 whole and an additional 60% of another whole.
Summary
In summary, 160% can be expressed as:
- Fraction: (\frac{8}{5})
- Mixed Number: (1 \frac{3}{5})
- Whole Number: It represents a value greater than 1, specifically 1.6 when converted to a decimal, which implies there is 1 full unit plus an additional part.
This process illustrates how to convert percentages into various numerical forms while maintaining clarity and precision in each step.