Question

Write each fraction or decimal as a percent. Round to the nearest tenth of a percent. $$\frac{19}{20}$$

Short answer

95%

Step-by-step solution

Convert the Fraction to a Decimal

Divide the numerator by the denominator to convert the fraction to a decimal. For the fraction \(\frac{19}{20}\), perform the division: \(19 \div 20 = 0.95\). So, \(\frac{19}{20} = 0.95\).

Convert the Decimal to a Percent

Multiply the decimal result by 100 to convert it to a percent. For \(0.95\), we have: \(0.95 \times 100 = 95\).

Round to the Nearest Tenth

Since there are no digits after the tenths place in 95, there is no need to round. So, the final answer is 95%.

Key concepts

Fraction to Decimal Conversion

Converting a fraction to a decimal is the first step in many math problems, including converting a fraction to a percentage. To do this, simply divide the numerator (the top number) by the denominator (the bottom number). For example, if we are given the fraction \(\frac{19}{20}\), we divide 19 by 20: 19 \div 20 = 0.95. So, \(\frac{19}{20} = 0.95\). This step is crucial because percentages are generally expressed in decimal form before conversion. Always remember to perform the division correctly for accurate results. If managing division is challenging, consider using a calculator for precision.

Decimal to Percent Conversion

Once you have the decimal equivalent of the fraction, the next step is to convert this decimal to a percentage. This can be done by multiplying the decimal by 100. For instance, with the decimal 0.95 obtained from converting \(\frac{19}{20}\), we multiply 0.95 by 100: \(0.95 \times 100 = 95\). This multiplication essentially shifts the decimal point two places to the right, giving us the percentage form. Thus, 0.95 as a decimal is 95% as a percentage. Remember, converting a decimal to a percentage always involves multiplying by 100, making the process straightforward.

Rounding to the Nearest Tenth

In some problems, you might need to round your result to the nearest tenth of a percent. Rounding helps in simplifying the percentage, especially when dealing with complex numbers. To round a number to the nearest tenth:

• Identify the digit in the tenths place.
• Look at the digit immediately to the right.
• If the next digit is 5 or more, round up the tenths place by one.
• If the next digit is less than 5, keep the tenths place as it is.

In our example, the percentage 95% does not have any digits after the tenths place. Therefore, no rounding is needed. However, understanding this concept is vital for scenarios requiring precision. Detailed rounding rules ensure accurate representation of percentages, especially in scientific and financial calculations.