Convert 4/15 to a decimal and a percent.
The Correct Answer and Explanation is:
To convert the fraction ( \frac{4}{15} ) to a decimal and a percent, let’s go through the steps methodically.
Step 1: Convert the Fraction to a Decimal
To convert the fraction ( \frac{4}{15} ) into a decimal, you perform division. This means dividing the numerator (4) by the denominator (15):
[
\frac{4}{15} = 4 \div 15
]
Using long division or a calculator, dividing 4 by 15 gives:
[
4 \div 15 = 0.2666\overline{6}
]
The result is a repeating decimal, where the digit 6 repeats indefinitely. To represent this in decimal form, we can write it as:
[
0.2666\overline{6}
]
Or, for simplicity, round it to two decimal places:
[
0.27
]
Thus, the decimal form of ( \frac{4}{15} ) is approximately 0.27.
Step 2: Convert the Decimal to a Percent
To convert the decimal to a percent, you multiply the decimal by 100 and add the percent sign (%). The calculation is:
[
0.27 \times 100 = 27
]
So, ( 0.27 ) as a percent is 27%.
Explanation:
The process involves two key steps: first, converting a fraction to a decimal by performing division, and second, converting the decimal to a percentage. In the first step, dividing the numerator (4) by the denominator (15) yields a repeating decimal, which reflects the fractional part of the number. The repeating decimal can be approximated by rounding to a certain number of decimal places. In the second step, multiplying the decimal by 100 gives the percentage form of the number, which is a useful way of expressing the relationship in terms of “per hundred.”
This method is applicable for any fraction you wish to convert to a decimal and percent. For fractions that result in repeating decimals, you can round them to the desired level of precision based on context (such as two decimal places for general use).