Decimals, Fractions, and Percents: Concepts & Practice

Chapter 1: Concepts Explained

1. Decimal Place Value and Rounding

Place Value: Each digit in a decimal has a place value based on its position. Example: In 3.726, 7 is in the tenths place.
Rounding: To round a decimal, look at the digit to the right of your place value. If it is 5 or greater, round up.

2. Changing Fractions to Decimals

Divide the numerator by the denominator. For example, 3/4 = 0.75.

3. Changing Decimals to Fractions

Write the decimal as a fraction with a denominator of 10, 100, 1000, etc., then simplify. Example: 0.6 = 6/10 = 3/5.

4. Comparing and Ordering Decimals

Line up the decimals by the decimal point and compare digit by digit.

5. Adding & Subtracting Decimals

Line up the decimal points vertically before adding or subtracting.

6. Adding & Subtracting Money

Treat money as decimals (e.g., $4.25 + $2.75 = $7.00).

7. Estimating Decimal Sums & Differences

Round decimals to the nearest whole number or tenth before adding or subtracting.

8. Multiplying Decimals & Money

Multiply as whole numbers, then count total decimal places for the answer.

9. Estimating Decimal Products

Round numbers before multiplying for a quick estimate.

10. Dividing Decimals

By Whole Numbers: Divide as usual, bring down decimal point.
By Decimals: Move decimal to make divisor a whole number, do the same to dividend, then divide.

11. Dividing Money

Divide as with decimals, keep track of the decimal point.

12. Estimating Decimal Quotients

Round numbers before dividing for a quick estimate.

13. Understanding Percent

Percent means “per hundred.” 25% = 25 out of 100 = 0.25.

14. Percents and Fractions

Write percent as a fraction over 100 and simplify. Example: 40% = 40/100 = 2/5.

15. Percents and Decimals

Move decimal point two places left to change percent to decimal. Example: 8% = 0.08.

16. Multiplying Percents and Fractions

Convert percent to decimal or fraction, then multiply.

Chapter 2: Worked Examples

Example 1: Round 4.678 to the nearest tenth.
Solution: The digit in the hundredths place is 7 (which is 5 or more), so round up. Answer: 4.7

Example 2: Change 7/8 to a decimal.
Solution: 7 ÷ 8 = 0.875

Example 3: Write 0.65 as a fraction in simplest form.
Solution: 0.65 = 65/100 = 13/20

Example 4: Add 0.23 + 0.7
Solution: 0.23 + 0.70 = 0.93

Example 5: Estimate 3.78 × 1.2
Solution: Round 3.78 to 4, 1.2 to 1. 4 × 1 = 4 (estimate)

Example 6: Divide $12.48 by 4
Solution: $12.48 ÷ 4 = $3.12

Example 7: What is 36% as a decimal and fraction?
Solution: 36% = 0.36 = 36/100 = 9/25

Example 8: Multiply 60% × 3/5
Solution: 60% = 0.6; 0.6 × 3/5 = 0.6 × 0.6 = 0.36