Understanding Decimals
Master place values, reading, writing, and comparing decimals
What You'll Learn
What Are Decimals?
Decimals are a way to express numbers that are not whole. They represent parts of a whole number using a decimal point (.) to separate the whole number part from the fractional part.
Understanding a Decimal Number
34.567
34
Whole number part
.
Decimal point
567
Decimal (fractional) part
Decimal Place Values
Each position to the right of the decimal point represents a fraction of 10:
| Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 2 | 4 | 5 | . | 3 | 6 | 8 |
In 245.368, each digit's value:
Reading and Writing Decimals
Two Methods for Reading Decimals
Method 1: Place Value Method
Read the whole number, say "and" for the decimal point, then read the decimal as a number followed by its place value.
3.45 → "three and forty-five hundredths"
12.7 → "twelve and seven tenths"
Method 2: Digit-by-Digit Method
Read each digit separately, saying "point" for the decimal.
3.45 → "three point four five"
12.7 → "one two point seven"
Money Example
Decimals are commonly used with money:
$24.75
= 24 dollars and 75 cents
= "twenty-four dollars and seventy-five cents"
Comparing Decimals
Steps to Compare Decimals
- 1 Line up the decimal points
- 2 Add zeros to make the same number of decimal places
- 3 Compare from left to right
Example: Compare 0.5 and 0.35
Step 1: Line up → 0.5 and 0.35
Step 2: Add zeros → 0.50 and 0.35
Step 3: Compare → 50 > 35
Answer: 0.5 > 0.35
Converting Decimals and Fractions
Decimal → Fraction
Use the place value as the denominator
0.5 = 5/10 = 1/2
0.25 = 25/100 = 1/4
0.125 = 125/1000 = 1/8
Fraction → Decimal
Divide numerator by denominator
1/2 = 1 ÷ 2 = 0.5
3/4 = 3 ÷ 4 = 0.75
1/5 = 1 ÷ 5 = 0.2
Rounding Decimals
The Rounding Rule
- • Look at the digit to the RIGHT of your rounding place
- • If it's 5 or more → round UP
- • If it's less than 5 → round DOWN
Example: Round 3.467 to the nearest tenth
Tenths place: 4
Next digit: 6 (≥5, so round up)
Answer: 3.5
Practice Problems
Test your understanding
1. What is the place value of 7 in 45.678? ▼
Hundredths (0.07 or 7/100)
2. Which is greater: 0.8 or 0.75? ▼
0.8 (0.80 > 0.75)
3. Convert 0.375 to a fraction ▼
3/8 (375/1000 simplified)
4. Round 8.649 to the nearest tenth ▼
8.6 (4 < 5, round down)
Common Mistakes to Avoid
- • Ignoring zeros: 0.5 and 0.50 are equal, but 0.5 and 0.05 are NOT
- • Comparing by length: 0.9 is greater than 0.87 (compare place by place)
- • Rounding errors: Always look at the digit to the RIGHT of your target place
- • Place value confusion: The first digit after the decimal is tenths, not ones
Key Takeaways
- ✓ Decimals express parts of whole numbers using place values
- ✓ Places after decimal: tenths, hundredths, thousandths
- ✓ To compare, line up decimal points and compare left to right
- ✓ Convert to fractions using place value as denominator
- ✓ Round by checking the digit to the right of target place
Related Lessons
Ready for Decimal Operations?
Now that you understand decimals, learn to add, subtract, multiply, and divide them!
