Problem 78 - Prealgebra

Question

Use a calculator to write each fraction as a decimal, and then change the decimal to a percent. Round all answers to the nearest tenth of a percent. $$\frac{8}{95}$$

Step-by-Step Solution

Answer

The fraction \( \frac{8}{95} \) is approximately 8.4%.

Step 1: Convert the Fraction to a Decimal

To convert the fraction \( \frac{8}{95} \) into a decimal, divide 8 by 95 using a calculator. This gives you approximately: \[ \frac{8}{95} \approx 0.0842105263 \]

Step 2: Change the Decimal to a Percentage

To convert the decimal you obtained from Step 1 to a percentage, multiply the decimal by 100. Using the approximate decimal from Step 1: \[ 0.0842105263 \times 100 = 8.42105263 \]

Step 3: Round to the Nearest Tenth of a Percent

Finally, round the percentage result from Step 2 to the nearest tenth of a percent. The value is 8.42105263, which rounds to 8.4% when rounded to the nearest tenth.

Key Concepts

Percent Conversion

Converting a decimal to a percent is an essential skill in math. You begin by understanding that a percent is simply a number out of 100. So, to convert a decimal to a percent, all you need to do is multiply the decimal by 100.
This is because percent means "per hundred." For example, with the decimal 0.0842105263, multiplying by 100 moves the decimal point two places to the right, resulting in 8.42105263. To make it clear:

• 0.1 as a percent is 10%.
• 0.25 as a percent is 25%.

So, for any decimal, just multiply by 100 and you have your percent!

Rounding Decimals

Rounding decimals helps simplify numbers, making them easier to understand and use. Here, it's about rounding to the nearest tenth of a percent.
You look at the second decimal place if only one is desired in the result. If the number is 5 or greater, round up by adding one to the first decimal place. If it's less than 5, keep the first decimal place the same.
For example:

• 8.42105263 rounds to 8.4% because the second decimal is a 2, which doesn't change the 4 in the first position.
• 8.456 would round to 8.5% because 5 is in the second decimal place.

Rounding makes numbers tidier and practical for use in everyday situations!

Calculator Usage

Using a calculator can transform how you convert fractions to decimals and then to percents with ease.
For example, to convert \( \frac{8}{95} \) into a decimal, you simply divide 8 by 95. A calculator helps by doing this quickly and accurately, giving you 0.0842105263.
Here are some tips:

• Ensure you're familiar with the division button on your calculator.
• Use parentheses if your calculator requires them for division.
• Check the display settings to ensure you see enough decimal places for accurate rounding.

A calculator is a great tool, especially for ensuring that conversions are precise and efficient, saving time while learning!