Decimals, Fractions, and Percents: A Comprehensive Guide

Table of Contents

1. Decimal Place Value and Rounding
2. Changing Fractions to Decimals
3. Changing Decimals to Fractions
4. Comparing and Ordering Decimals
5. Adding Decimals
6. Subtracting Decimals
7. Adding and Subtracting Money
8. Estimating Decimal Sums and Differences
9. Multiplying Decimals
10. Multiplying Money
11. Estimating Decimal Products
12. Dividing Decimals by Whole Numbers
13. Dividing Whole Numbers by Decimals
14. Dividing Decimals by Decimals
15. Dividing Money
16. Estimating Decimal Quotients
17. Understanding Percent
18. Percents and Fractions
19. Percents and Decimals
20. Multiplying Percents and Fractions

Key Concepts Explained

1. Decimal Place Value and Rounding
   Each digit in a decimal has a value based on its position (tenths, hundredths, thousandths, etc). Rounding means making a decimal simpler while keeping its value close.
2. Changing Fractions to Decimals
   Divide the numerator (top number) by the denominator (bottom number).
3. Changing Decimals to Fractions
   Write the decimal as a fraction with a denominator as a power of 10, then simplify.
4. Comparing and Ordering Decimals
   Line up decimals by the decimal point and compare digits from left to right.
5. Adding/Subtracting Decimals
   Line up decimal points, add or subtract as whole numbers, and keep the decimal point in the answer.
6. Adding/Subtracting Money
   Treat money amounts as decimals (e.g., $3.25 + $2.10).
7. Estimating Decimal Sums/Differences
   Round numbers before adding or subtracting to make mental math easier.
8. Multiplying Decimals
   Multiply as whole numbers, then count total decimal places in the factors and place in the product.
9. Multiplying Money
   Multiply as decimals, keep two decimal places (cents).
10. Estimating Decimal Products
    Round decimals before multiplying for a quick estimate.
11. Dividing Decimals
    For divisor as a decimal, move the decimal to the right in both divisor and dividend until divisor is a whole number, then divide.
12. Dividing Money
    Divide as decimals, keep two decimal places (cents).
13. Estimating Decimal Quotients
    Round numbers before dividing for quick estimation.
14. Understanding Percent
    Percent means “per 100”. 35% = 35 out of 100 = 0.35.
15. Percents and Fractions
    Write percent as a fraction over 100 and simplify.
16. Percents and Decimals
    To convert percent to decimal, divide by 100 or move decimal left two places.
17. Multiplying Percents and Fractions
    Convert percent to a fraction or decimal first, then multiply.

Worked Examples

1. Rounding 4.678 to the nearest hundredth:
   Look at the thousandths place (8). Since it's 5 or more, round up: 4.68.
2. Change 3/4 to a decimal:
   3 ÷ 4 = 0.75
3. Change 0.6 to a fraction:
   0.6 = 6/10 = 3/5
4. Compare: 0.56 vs 0.506
   0.56 is greater because 5 tenths and 6 hundredths is more than 5 tenths and 0 hundredths.
5. Add: 2.45 + 3.6
   2.45
   +3.60
   =5.05
6. Subtract: 8.9 - 2.34
   8.90
   -2.34
   =6.56
7. Add money: $3.25 + $1.75
   = $5.00
8. Estimate: 4.7 + 3.2
   Round to 5 + 3 = 8
9. Multiply: 0.3 × 0.2
   3 × 2 = 6. There are 2 decimal places, so answer is 0.06
10. Multiply money: $4.50 × 3
    $4.50 × 3 = $13.50
11. Estimate: 2.9 × 1.1
    3 × 1 = 3
12. Divide: 1.2 ÷ 3
    1.2 ÷ 3 = 0.4
13. Divide: 6 ÷ 0.2
    6 ÷ 0.2 = 30
14. Divide: 0.81 ÷ 0.09
    Move decimals: 81 ÷ 9 = 9
15. Divide money: $12.00 ÷ 4
    $12.00 ÷ 4 = $3.00
16. Estimate: 8.2 ÷ 2.1
    8 ÷ 2 = 4
17. 35% as a decimal:
    35 ÷ 100 = 0.35
18. 80% as a fraction:
    80/100 = 4/5
19. 0.6 as a percent:
    0.6 × 100 = 60%
20. Find 25% of 80:
    25% = 0.25; 0.25 × 80 = 20

Pre-Test: Multiple Choice (40 Questions)

Questions & Answers (Based on Your Pre-Test)

Post-Test: Multiple Choice (40 Questions)