On a scavenger hunt, you find 19 out of 20 objects. Write “19 out of 20” as a fraction, a decimal, and a percent
The Correct Answer and Explanation is:
To express “19 out of 20” as a fraction, decimal, and percent, let’s break it down:
1. Fraction:
The phrase “19 out of 20” is already given in fractional form. The fraction is simply:
[
\frac{19}{20}
]
This represents 19 objects found out of a total of 20.
2. Decimal:
To convert the fraction (\frac{19}{20}) into a decimal, we divide the numerator (19) by the denominator (20):
[
\frac{19}{20} = 0.95
]
Thus, the decimal representation of “19 out of 20” is 0.95.
3. Percent:
To convert a decimal into a percentage, we multiply the decimal by 100 and add the percent sign. So, for 0.95, the calculation is:
[
0.95 \times 100 = 95\%
]
Therefore, “19 out of 20” as a percentage is 95%.
Explanation:
Fractions, decimals, and percentages are three ways of representing parts of a whole. All of these representations are different forms of expressing a ratio between two quantities, and the conversion between them follows straightforward mathematical principles.
- Fraction: A fraction shows how many parts of a whole are considered. In this case, ( \frac{19}{20} ) shows that 19 out of 20 objects were found, so it is already in the correct form.
- Decimal: A decimal represents the fraction as a part of 1. To convert ( \frac{19}{20} ) into a decimal, you divide 19 by 20, which equals 0.95. This decimal value is a way to express the proportion of objects found in terms of a base of 1.
- Percent: A percent represents a fraction out of 100. To convert the decimal (0.95) into a percentage, you multiply by 100 to get 95%. This is a convenient way to express proportions in terms of 100, which is a common scale used in everyday life (e.g., test scores, performance, etc.).
In summary, “19 out of 20” can be expressed as:
- Fraction: ( \frac{19}{20} )
- Decimal: 0.95
- Percent: 95%