Problem 68 - Prealgebra

Question

Write as a percent. Round to the nearest tenth of a percent. $$\frac{7}{8}$$

Step-by-Step Solution

Answer

87.5%

Step 1: Convert the Fraction to Decimal

To convert the fraction \( \frac{7}{8} \) into a decimal, divide 7 by 8. Performing the division, we get 7 divided by 8 equals 0.875. Therefore, \( \frac{7}{8} = 0.875 \).

Step 2: Convert Decimal to Percent

To convert the decimal \(0.875\) to a percent, multiply it by 100. Therefore, \(0.875 \times 100 = 87.5\).

Step 3: Round to the Nearest Tenth

Rounding 87.5 to the nearest tenth of a percent gives us the same value, 87.5%.

Key Concepts

Fraction to Decimal Conversion

Converting a fraction to a decimal is fundamental in mathematics. It is typically done when you take the numerator, or the "top" part of the fraction, and divide it by the denominator, the "bottom" part. For example, consider the fraction \(\frac{7}{8}\). By dividing 7 by 8, you perform the operation using either long division or a calculator. When using long division, you'd set it up by placing 7 under the division bar and 8 outside as the divisor. Working through the division, you end up with 0.875. So, \(\frac{7}{8} = 0.875\). This decimal representation is often used because it can be more intuitive in certain calculations and makes further operations, like converting to percentages, easier.

Decimal to Percent Conversion

After converting a fraction to a decimal, the next step might be to convert this decimal into a percent. This process helps us understand proportions in everyday terms, like discounts, and probabilities. To convert a decimal like 0.875 to a percent, you simply multiply by 100.

• 0.875 multiplied by 100 equals 87.5.

The multiplication by 100 shifts the decimal point two places to the right, transforming it from a simple decimal into a percentage. Essentially, you're scaling the number from a 'part of one' to a 'part of one hundred,' which is what a percent represents. That's how you turn 0.875 into 87.5%.

Rounding Decimals

When you encounter decimals in calculations, particularly percentages, rounding to a specific decimal place can make these numbers easier to communicate and understand. Rounding is the process of keeping the number concise without altering its value significantly.

• To round to the nearest tenth, observe the number in the hundredths place.
• If it's 5 or greater, round up the tenths place.
• If it's less than 5, keep the tenths place as it is.

For instance, with the number 87.5%, it already ends in a ".5" so there is no need to adjust as it is already at the nearest tenth. This step ensures your final result is clean and fits the context in which you are presenting it.