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Chapter 6: Problem 70

In the following exercises, convert each fraction to a percent. $$\frac{9}{8}$$

Short Answer

Expert verified
112.5%

Step by step solution

01

- Understand the Fraction

We need to convert the fraction \(\frac{9}{8}\) into a percent. Percent means per hundred, so we need to find how many out of 100 this fraction represents.
02

- Convert the Fraction to a Decimal

To convert \(\frac{9}{8}\) to a decimal, divide the numerator (9) by the denominator (8). \(9 \div 8 = 1.125\).
03

- Convert the Decimal to a Percent

To convert the decimal \(1.125\) to a percent, multiply it by 100. \(1.125 \times 100 = 112.5\). This means \(\frac{9}{8}\) is 112.5\%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

fractions
A fraction represents a part of a whole. It consists of two numbers鈥攖he numerator and the denominator. The numerator is the top number and tells us how many parts we have. The denominator is the bottom number and tells us how many equal parts the whole is divided into. For example, in the fraction \(\frac{9}{8}\), 9 is the numerator and 8 is the denominator. Fractions can be greater than, less than, or equal to 1.
Fractions greater than 1, like our example, have numerators larger than their denominators. These are called improper fractions.
To work with fractions effectively, we often convert them to decimals or percents.
decimal conversion
To convert a fraction to a decimal, we divide the numerator by the denominator. This process turns the fraction into a number that is easier to understand and work with.
For example, to convert the fraction \(\frac{9}{8}\) to a decimal, we perform the division 9 梅 8, which equals 1.125.
Decimal conversion is especially helpful in various mathematical calculations and when comparing numbers.
Understanding how to move between fractions and decimals is crucial for solving many types of math problems.
percent calculation
A percent is a way of expressing a number as a part of 100. To convert a decimal to a percent, we multiply the decimal by 100.
In our example, the decimal 1.125 is multiplied by 100 to get 112.5%. Essentially, this means that \(\frac{9}{8}\) is equivalent to 112.5 out of 100.
Here鈥檚 a simple rule to remember: when converting from decimal to percent, just move the decimal point two places to the right and add a percent sign.
Understanding percent calculation is essential because percents are frequently used in everyday life, such as in discounts, interest rates, and statistics.

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Most popular questions from this chapter

In the following exercises, find the rate of commission. Ruben received \(\$ 675\) commission when he sold a \(\$ 4,500\) painting at the art gallery where he works. What was the rate of commission?

Determine whether each equation is a proportion. $$ \frac{12}{18}=\frac{6.99}{10.99} $$

Solve the applications of percents. Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. She wants to leave 16% of the total bill as a tip. How much should the tip be?

The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat?

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