Working with Decimals (Introduction)
Understand how decimal points extend place value into parts smaller than one — the foundation of money, measurement, and precise calculation.
Every price, paycheck, and measurement uses decimals. Your GPA, your speed on a run, your gas mileage — all decimals. They represent the space between whole numbers with precision. Misplace a decimal point, and $4.99 becomes $49.90. That mistake happens every day.
- Identify decimal place values: tenths, hundredths, thousandths
- Convert between decimals and fractions
- Add and subtract decimals by aligning the decimal point
Decimals extend the place value system to the right of the decimal point. Each place to the right is ten times smaller than the place to its left — just like each place to the left is ten times larger.
A decimal is a fraction whose denominator is a power of 10: \(0.3 = \frac{3}{10}\), \(0.75 = \frac{75}{100}\), \(0.004 = \frac{4}{1000}\).
Decimal Place Value Chart
Decimal Place Value — extending Lesson 1
| Hundreds | Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 100s | 10s | 1s | • | 0.1s | 0.01s | 0.001s |
| 1 | 2 | 4 | . | 7 | 5 | 0 |
| 100 | 20 | 4 | 7/10 | 5/100 | 0 |
124.75 = 100 + 20 + 4 + 7/10 + 5/100 | The decimal point is the boundary between whole and part
You have $1.25. What does each digit represent?
- 1 → ones place → one whole dollar
- 2 → tenths place → 2 dimes (two-tenths of a dollar)
- 5 → hundredths place → 5 pennies (five-hundredths of a dollar)
Convert 0.75 to a fraction in lowest terms.
0.75 is in the hundredths place (two places right of decimal):
\[ 0.75 = \frac{75}{100} = \frac{3}{4} \]Divide numerator and denominator by 25 to simplify.
Brand A: $3.79 per pound. Brand B: $3.7 per pound. Which is cheaper?
Align the decimal places: $3.79 vs $3.70.
\[ 3.70 < 3.79 \]Brand B is cheaper by $0.09 per pound — remember, 3.7 and 3.70 are the same value.
Try these:
- What is the value of the digit 4 in 12.045?
- Convert 0.6 to a fraction.
- Which is larger: 0.9 or 0.10?
▶ Show Answers
- 4 hundredths (0.04) — it's in the second place right of the decimal.
- \(\frac{6}{10} = \frac{3}{5}\)
- 0.9 is larger — 0.9 = 0.90 = 90 hundredths, vs 0.10 = 10 hundredths.
- Moving the decimal by accident: 0.5 and 5.0 are not the same. 5.0 is ten times larger. When adding or multiplying, always track the decimal point carefully.
- Thinking 0.10 > 0.9: 10 > 9 as whole numbers, but 0.10 < 0.9. Compare by place value starting from the tenths: 9 tenths > 1 tenth.
- Misaligning decimal points when adding: Stack numbers so decimal points are directly above each other. 12.5 + 3.75 means 12.50 + 3.75, not 12.5 + 37.5.
- The decimal point divides whole from part — left is whole, right is fractional.
- Each place right is 10× smaller — tenths, hundredths, thousandths...
- Trailing zeros don't change value — 0.50 = 0.5 = 5/10.
- Always align decimal points when adding or subtracting decimal numbers.
Engineers specify tolerances in thousandths of an inch (0.001"). Medical professionals measure in decimals — a prescribed dose of 0.5mg vs 5.0mg is a 10× difference that can be life-threatening. Decimal precision is not optional in technical fields.
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Working with Decimals (Introduction) — Quiz
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