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# 1.5: Review of Decimals and Percents

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Skills to Develop

• Convert fractions to decimals and back.
• Perform operations with decimals.
• Round off decimals to a given place.
• Define a percent.
• Convert percents to decimals and back.
• Convert fractions to percents and back.

## Decimals

In this section, we provide a brief review of the decimal system. A real number in decimal form, a decimal consists of a decimal point, digits ($$0$$ through $$9$$) to the left of the decimal point representing the whole number part, and digits to the right of the decimal point representing the fractional part. The digits represent powers of 10 as shown in the set $$\{…, 1,000, 100, 10, 1, 1/10, 1/100, 1/1,000, …\}$$according to the following diagram:

Figure 1.5.1

For example, the decimal 538.3 can be written in the following expanded form:

$$5 \cdot \color{Cerulean}{100} \color{Black}{+} 3 \cdot \color{Cerulean}{10} \color{Black}{+} 8 \cdot \color{Cerulean}{1} \color{Black}{+} 3 \cdot \color{Cerulean}{\frac{1}{10}}$$

After simplifying, we obtain the mixed number $$528 \frac{3}{10}$$. Use this process to convert decimals to mixed numbers.