Question

Write each fraction as a percent. $$\frac{3}{4}$$

Short answer

Answer: The equivalent percentage of the fraction $$\frac{3}{4}$$ is $$75\%$$.

Step-by-step solution

Convert the fraction to a decimal

Divide the numerator by the denominator to convert it into a decimal: $$\frac{3}{4} = 0.75$$

Convert the decimal to a percent

Multiply the decimal by 100 to get the percentage: $$0.75 \times 100 = 75$$

Add the percent sign

Include the percent sign to the answer: $$75\%$$ The fraction $$\frac{3}{4}$$ is equal to $$75\%$$.

Key concepts

Decimal Conversion

Converting a fraction into a decimal is a straightforward process. The key is to understand that a fraction is essentially a division of two numbers. These numbers are known as the numerator and the denominator. For example, in the fraction \( \frac{3}{4} \), 3 is the numerator, and 4 is the denominator. To convert this fraction into a decimal, you divide the numerator (3) by the denominator (4). When you perform this division, you'll find that \( 3 \div 4 = 0.75 \). Now, you have successfully converted the fraction \( \frac{3}{4} \) into the decimal 0.75.

There are some tips to make this easier:

• Always ensure your division setup is correct, numerator divided by the denominator.
• If your division doesn’t end, you may have a repeating decimal. Use a calculator for efficiency.

Percentage Calculation

Once a fraction is expressed as a decimal, the next step involves converting this decimal into a percentage. Percent means per hundred, so moving from decimals to percentages involves comparing the decimal to 100. The straightforward method is multiplying the decimal by 100.

Let’s continue with our example: we have the decimal 0.75. To convert that into a percentage, multiply 0.75 by 100 and you get 75. Thus, \( 0.75 \times 100 = 75 \). Now, our decimal has transformed into a nice round number signifying a percentage value.

Using this method:

• Multiplying by 100 effectively shifts the decimal point two places to the right.
• This operation is consistent for any decimal you wish to convert to a percentage.

Percent Sign

Adding the percent sign is a crucial final touch in expressing values as percentages. It's a small symbol, but it holds significant meaning, indicating that the number is a percentage. When representing a number as a percentage, the percent sign (%) is always placed immediately after the number.

Continuing from our example, after calculating that 0.75 turns into 75 through multiplication, the last step is to attach a percent sign. Hence, the final representation is 75%, which tells us that we're dealing with a percentage of a whole.

Key things to remember about the percent sign:

• It helps to communicate clearly that the number is a percentage, not a decimal or another format.
• In mathematical information and real-world data, percentages offer a familiar way to express ratios and comparisons.