Problem 30 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth,if necessary. $$\frac{7}{25}$$

Step-by-Step Solution

Answer

28%

Step 1: Understanding Percent

To convert a fraction to a percent, we need to multiply the fraction by 100. This is because 'percent' means 'per one hundred.'

Step 2: Converting Fraction to Decimal

We start by dividing the numerator by the denominator. So, for \( \frac{7}{25} \), we divide 7 by 25 to get 0.28.

Step 3: Converting Decimal to Percent

Now that we have the decimal, which is 0.28, we convert it to a percent by multiplying by 100. So, \( 0.28 \times 100 = 28 \).

Step 4: Rounding and Final Result

Since 28.0 is already a whole number, there's no need to round. The final percentage is 28%.

Key Concepts

Converting Fractions to Decimals

Converting a fraction to a decimal is essentially dividing the numerator by the denominator. This process transforms the fraction into a decimal number. In our example, the fraction \( \frac{7}{25} \) means dividing 7 by 25. Performing this division results in 0.28, a decimal number. Key things to remember:

• Divide the top number (numerator) by the bottom number (denominator).
• This conversion simplifies the representation of quantities.
• It often makes further calculations easier.

Fractions like \( \frac{1}{2} \), which is 0.5 as a decimal, highlight how fractions can be visualized as parts of a whole.

Converting Decimals to Percent

Once you have a decimal, turning it into a percent is straightforward. The word "percent" literally means "per one hundred." Therefore, to convert a decimal to a percent, you simply multiply the decimal number by 100.

• If you start with 0.28 as a decimal, multiplying by 100 gives you 28.
• This conversion essentially shifts the decimal point two places to the right.
• This process is handy for understanding proportions out of 100, which is common in data analysis.

Remember that converting to percent is useful for expressing how large a number is relative to 100.

Understanding Mathematical Rounding

Rounding numbers is a technique to simplify results while maintaining an acceptable level of accuracy. We often round to the nearest tenth, whole number, or other designated place value based on the problem context.

• Check the digit right after the place you want to round to.
• If this digit is 5 or more, round up the target digit by one. Otherwise, leave it as is.
• In our example, 28.0 becomes 28 since there are no extra digits to influence the rounding.

Rounding ensures that numbers are easy to work with without straying too far from the actual value.