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Grade 5 Math Lab: The Bridge to Algebra FREE
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Decimal Place Value & Operations
Learning Objectives
- Understand decimal place value to thousandths
- Add and subtract decimals fluently
- Compare and order decimals using place value
- Round decimals to any place
Key Concepts
Decimal
A number that uses a decimal point to show tenths, hundredths, thousandths, and beyond
Tenths
The first place after the decimal point (0.1 = 1/10)
Hundredths
The second place after the decimal point (0.01 = 1/100)
Thousandths
The third place after the decimal point (0.001 = 1/1000)
Theory
Decimals are an extension of our base-10 place value system. Just as we move left for larger values (tens, hundreds), we move right for smaller values (tenths, hundredths, thousandths).
**The Fractal Nature of Decimals:**
When you zoom into any segment of a number line, you can always find more numbers! Between 0.1 and 0.2, there are 0.11, 0.12, 0.13... and between those, even more!
**Place Value Chart:**
```
Ones | . | Tenths | Hundredths | Thousandths
3 | . | 4 | 5 | 6
```
The number 3.456 = 3 + 0.4 + 0.05 + 0.006
**Adding & Subtracting Decimals:**
1. Line up the decimal points vertically
2. Add zeros as placeholders if needed
3. Add or subtract as with whole numbers
4. Bring the decimal point straight down
Examples
Compare 0.35 and 0.305
Solution: 0.35 > 0.305 (think: 0.350 vs 0.305, comparing hundredths: 5 > 0)
12.456 + 3.7
Solution: Line up: 12.456 + 3.700 = 16.156
Round 4.678 to the nearest tenth
Solution: 4.7 (look at hundredths: 7 ≥ 5, round up)
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Knowledge Check
Test your understanding of Fractal Number Line!