Decimals, Fractions, and Percents: Concepts and Practice

Chapter 1: Concepts Explained

1. Decimal Place Value and Rounding

Each digit in a decimal number has a place value based on its position. For example, in 3.476:

To round a decimal, look at the digit to the right of the place value you are rounding to. If it's 5 or greater, round up; otherwise, round down.

2. Changing Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 0.75.

3. Changing Decimals to Fractions

Write the decimal as a fraction with the appropriate denominator, then simplify. For example, 0.6 = 6/10 = 3/5.

4. Comparing and Ordering Decimals

Line up the decimals and compare the digits from left to right, starting with the highest place value.

5. Adding and Subtracting Decimals

Align the decimal points and add or subtract as with whole numbers. Fill in zeros if necessary.

6. Multiplying Decimals

Multiply as with whole numbers, then count total decimal places in both numbers and place the decimal accordingly in the answer.

7. Dividing Decimals

Move the decimal point in the divisor and dividend to make the divisor a whole number, then divide as usual.

8. Understanding Percent

Percent means “per hundred.” 45% means 45 out of 100, or 0.45.

Chapter 2: Examples

1. Rounding: Round 3.478 to the nearest hundredth.
Solution: Look at the thousandths (8). 8 ≥ 5, so round up: 3.48 becomes 3.48 + 0.01 = 3.48.
2. Fraction to Decimal: 7/8 = 7 ÷ 8 = 0.875
3. Decimal to Fraction: 0.25 = 25/100 = 1/4
4. Comparing Decimals: Which is greater, 0.65 or 0.605?
Solution: Compare in hundredths: 0.65 > 0.605.
5. Adding Decimals: 1.34 + 2.6 = 3.94
6. Multiplying Decimals: 0.7 × 0.3 = 0.21 (two decimal places)
7. Dividing Decimals: 1.2 ÷ 0.4 = (Move decimal in 0.4 to make it 4, do the same to 1.2 to make it 12) ⇒ 12 ÷ 4 = 3
8. Percent to Fraction: 60% = 60/100 = 3/5

Chapter 3: Pre-Test (Multiple Choice)

  1. What is 0.37 in words?


  2. Round 8.436 to the nearest tenth.


  3. What is 5/8 as a decimal?


  4. Which is 0.4 as a fraction in lowest terms?


  5. Which is greater?


  6. What is 2.56 + 3.7?


  7. What is 4.8 - 1.13?


  8. What is $5.75 + $2.30?


  9. Estimate: 3.78 + 2.26


  10. Multiply: 0.6 × 0.5


Chapter 4: Questions & Answers

Q: What is the tenths place in the number 4.57?
A: The tenths place is 5.
Q: How do you convert 1/2 to a decimal?
A: Divide 1 by 2 to get 0.5.
Q: What is 0.6 as a fraction in simplest form?
A: 0.6 = 6/10 = 3/5.
Q: How do you compare 0.78 and 0.8?
A: 0.8 is greater than 0.78.
Q: How do you multiply 0.3 by 0.2?
A: Multiply as whole numbers (3 × 2 = 6), then place decimal (two places): 0.06.
Q: What is 25% as a decimal and as a fraction?
A: 25% = 0.25 = 1/4.

Chapter 5: Post-Test (Multiple Choice)

  1. What is 0.94 in words?


  2. Round 2.589 to the nearest tenth.


  3. What is 3/5 as a decimal?


  4. Which is 0.7 as a fraction in lowest terms?


  5. Which is greater?


  6. What is 4.25 + 1.69?


  7. What is 6.5 - 2.42?


  8. What is $3.55 + $6.45?


  9. Estimate: 7.18 + 1.86


  10. Multiply: 0.8 × 0.4