Problem 74 - Algebra 1: Concepts and Skills

Question

Write the fraction as a percent. $$ \frac{9}{10} $$

Step-by-Step Solution

Answer

The fraction \( \frac{9}{10} \) as a percent is 90%.

Step 1: Express the fraction as a decimal

To convert a fraction to a decimal, the numerator of the fraction is divided by the denominator. In this case, divide 9 (the number on top), by 10(the number at the bottom). Therefore, \( \frac{9}{10} = 0.9 \)

Step 2: Convert the decimal to a percentage

Multiply the decimal by 100 to get the percentage. For example, to convert 0.9 to a percent, multiply 0.9 by 100, you will get 90.

Key Concepts

Decimal Conversion

Understanding the conversion of fractions into decimals is a fundamental skill in mathematics. It is especially useful in everyday life, where measurements, money, and statistical data often require us to switch between these two forms. To convert a fraction to a decimal, one simply divides the numerator by the denominator.

For instance, when we look at the fraction \( \frac{9}{10} \), the numerator is 9, and the denominator is 10. When we divide 9 by 10 using long division or a calculator, the result we get is 0.9. This indicates that the fraction \( \frac{9}{10} \) is equivalent to 0.9 when expressed as a decimal. Learning this conversion process enables students to perform further numerical operations and applications in real life scenarios.

Numerical Operations

Once you understand how to convert fractions into decimals, the next step is performing numerical operations with these decimals. Mathematical operations such as addition, subtraction, multiplication, and division remain consistent whether you're working with whole numbers, fractions, or decimals. However, working with decimals can sometimes be more straightforward, as they easily align with our base-10 system of counting.

It's important to handle decimals correctly in order to maintain accuracy. For multiplication, as we see in converting decimals to percentages, we use the concept that 100% is equivalent to the whole or '1' in decimal form. Hence, multiplying any decimal by 100 shifts its value from a part of a whole to a percentage. For example, multiplying the decimal 0.9 by 100 gives us 90, which can be interpreted as 90% of a whole.

Percent Calculations

Percentages are a vital part of daily mathematics, used to represent data in areas such as finance, statistics, and even when grading tests. A percentage is essentially a fraction with a denominator of 100, making it a part of this standardized scale.

When converting a decimal to a percentage, we are, in effect, scaling the decimal by a factor of 100. By multiplying the decimal 0.9 by 100, we expand it to its equivalent portion out of 100, which is 90%. In reverse, to convert a percentage to a decimal, divide by 100. This is invaluable when you wish to perform operations with percentages; converting them into decimals can sometimes simplify these operations. For example, finding 20% of a quantity is easier when you convert 20% to 0.2 and then multiply it by the quantity in question.