Problem 75 - Algebra 1

Question

Write the fraction as a decimal and as a percent. $$ \frac{5}{8} $$

Step-by-Step Solution

Answer

The decimal form of \( \frac{5}{8} \) is 0.625 and the percent form is 62.5%.

Step 1: Convert fraction to decimal

To convert the fraction \(\frac{5}{8}\) to a decimal, divide 5 by 8. This can be done using a calculator or long division. The result is 0.625

Step 2: Convert decimal to percent

To next convert this decimal to a percent, multiply it by 100, thus 0.625 * 100 which equals 62.5%

Key Concepts

Percent Conversion

When you see a number expressed as a percent, remember that it represents a part out of 100. Turning a decimal into a percent is a simple task once you understand this basic idea. To convert a decimal to a percent, all you need to do is multiply the decimal by 100. This process effectively shifts the decimal point two places to the right.
For example, if we have the decimal 0.625, we multiply it by 100 to get 62.5. Essentially,

• 0.625 becomes 62.5% when multiplied by 100.
• This indicates that 0.625 is the same as 62.5 parts out of 100.

Percent conversion allows you to compare and understand parts of a whole in an easy-to-visualize form.

Division

Division is essential for converting a fraction into a decimal. Essentially, you are determining how many times the denominator can fit into the numerator. This process can be done using a calculator or by hand using long division. Let's break it down with \[\frac{5}{8}\].

• Here, you divide 5 by 8. Since 5 is smaller than 8, the answer will be less than 1.
• 0.625 comes from this division, meaning 5 divided by 8 equals 0.625.

Long division involves using place values to calculate the quotient when a divisor cannot fit into the dividend perfectly. If you’re dividing by hand, you might encounter recurring decimals. For exact decimals, like 0.625, the division completes after a few steps.

Fraction Decimal Conversion

Transforming a fraction into a decimal is a straightforward yet crucial skill in math. This involves understanding the relationship between the numerator and the denominator. To convert \[\frac{5}{8}\] into a decimal:

• Start with division: the numerator (5) divided by the denominator (8).
• The division will yield 0.625 exactly, as explained earlier.

Recognizing that fractions can be expressed as decimals is valuable for a variety of math tasks, making it easier to compare values and perform calculations. Knowing both forms of a number allows you to switch between formats based on what the problem requires or prefer.