Decimals, Fractions, and Percents: A Complete Guide
Master decimal operations, fractions, and percents with explanations, examples, and practice tests.
Key Concepts Explained
Decimal Place Value and Rounding:
Each digit in a decimal has a place value (tenths, hundredths, thousandths, etc.). Rounding means making a decimal simpler but keeping its value close.
Changing Fractions to Decimals:
Divide the numerator by the denominator. Example: 3/4 = 0.75.
Changing Decimals to Fractions:
Write the decimal as a fraction with 10, 100, 1000, etc., as the denominator and simplify.
Comparing and Ordering Decimals:
Line up decimals by the decimal point; compare from left to right.
Adding & Subtracting Decimals:
Align decimal points before operating.
Estimating Decimal Sums and Differences:
Round decimals before adding or subtracting to get an estimate.
Multiplying Decimals:
Multiply as whole numbers, then count total decimal places in factors and place the decimal point in the product.
Estimating Decimal Products:
Round the numbers before multiplying.
Dividing Decimals:
If dividing by a decimal, make the divisor a whole number by multiplying both by 10, 100, etc.
Understanding Percents:
Percent means "per hundred." 45% = 45 out of 100.
Percents, Fractions, and Decimals:
Convert between them by dividing or multiplying by 100.
Worked Examples
Rounding Decimals: Round 3.786 to the nearest hundredth:
Look at the thousandths (6). Since 6 >= 5, round up: 3.79
Fraction to Decimal: 5/8 = 0.625 (5 ÷ 8)
Decimal to Fraction: 0.2 = 2/10 = 1/5
Comparing Decimals:
Which is greater: 0.57 or 0.507?
0.57 > 0.507
Adding Decimals: 4.3 + 2.15 = 6.45
Subtracting Decimals: 7.25 - 1.9 = 5.35
Estimating Decimal Sums:
2.68 + 5.14 ≈ 3 + 5 = 8
Multiplying Decimals: 0.6 × 0.4 = 0.24
Dividing Decimals by Whole Numbers: 4.8 ÷ 3 = 1.6
Dividing Whole Numbers by Decimals: 6 ÷ 0.2 = 30
Percent to Decimal:
25% = 0.25 (divide by 100)
Decimal to Percent:
0.85 = 85% (multiply by 100)
Multiplying Percents and Fractions:
25% of 32 = 0.25 × 32 = 8