Question

Write each fraction or decimal as a percent. Round to the nearest tenth of a percent. $$\frac{3}{71}$$

Short answer

4.2%

Step-by-step solution

Convert Fraction to Decimal

To convert the fraction \(\frac{3}{71}\) to a decimal, divide the numerator by the denominator: \(\frac{3}{71} \approx 0.0422535\).

Convert Decimal to Percent

To convert the decimal 0.0422535 to a percent, multiply by 100: \(0.0422535 \times 100 = 4.22535\).

Round to the Nearest Tenth

Round 4.22535 to the nearest tenth. Look at the digit in the hundredths place, which is 2. Since it is less than 5, the digit in the tenths place remains 2. Therefore, 4.22535 rounded to the nearest tenth is 4.2.

Key concepts

Fraction to Decimal

To convert a fraction to a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). In this exercise, we converted the fraction \( \frac{3}{71} \) by dividing 3 by 71. This gives us a decimal value of approximately \( 0.0422535 \).
Using a calculator, you would input 3 ÷ 71 to get this value.
Understanding this step is crucial, as many math problems involve moving between fractions and decimals.

Decimal to Percent

Once you have a decimal, converting it to a percent is easy. Just multiply the decimal by 100.
For example, to convert \( 0.0422535 \) to a percent, you multiply it by 100: \( 0.0422535 \times 100 = 4.22535 \).
The reason we multiply by 100 is because 'percent' means 'per hundred,' so essentially we're scaling up our decimal to a value out of 100.
This concept is fundamental in various applications, such as statistics and real-world problems involving percentages.

Rounding Decimals

Rounding decimals is an essential skill to make numbers more manageable and easier to understand.
In our example, we had \( 4.22535 \) and needed to round it to the nearest tenth.
To round to the nearest tenth, you look at the hundredths place (the second digit to the right of the decimal point).
If that digit is 5 or greater, you round up. If it's less than 5, you round down.
Here, the hundredths place is 2, which is less than 5, so we leave the tenths place as 2.
Thus, \( 4.22535 \) rounded to the nearest tenth is \( 4.2 \).
Rounding is often used in reporting data to make it more readable and to simplify complex numbers.