Question

Vocabulary Terms - Define/Illustrate

Before you add or subtract decimals, what must you do?

Why?




Words that tell you to subtract:

In 2012, the population of NY was about 2.4 x 10^7 and the population of Oregon was 4 x 10^5.
How many more people live in NY than in Oregon?


4.29 x 10^8 - 1.68 x 10^4 =

5.08 x 10^-4 - 3.12 x 10^-5 =

Answer 1

### Vocabulary Terms - Definitions/Illustrations

**Before you add or subtract decimals, what must you do?**
- **Align the Decimals**: Before adding or subtracting decimals, you must ensure that the numbers are aligned correctly by their decimal points. This means writing the numbers in such a way that their decimal places are directly beneath each other.

**Why?**
- **Precision**: Aligning the decimals ensures that each digit is in the correct place value position (ones, tenths, hundredths, etc.). This is crucial for performing accurate addition or subtraction, as misalignment can lead to significant errors in the results.

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### Words that tell you to subtract:
Some common phrases that indicate subtraction include:
- "find the difference"
- "how many fewer"
- "less than"
- "subtract"

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### Example Problem:
**In 2012, the population of NY was about 2.4 x 10^7 and the population of Oregon was 4 x 10^5. How many more people live in NY than in Oregon?**

1. **Convert Scientific Notation**:
- NY population: \( 2.4 \times 10^7 = 24,000,000 \)
- Oregon population: \( 4 \times 10^5 = 400,000 \)

2. **Subtraction**:
- Difference: \( 24,000,000 - 400,000 = 23,600,000 \)

**So, there are 23,600,000 more people living in NY than in Oregon.**

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### Calculations:
1. **\( 4.29 \times 10^8 - 1.68 \times 10^4 \)**
- Convert to standard form:
- \( 4.29 \times 10^8 = 429,000,000 \)
- \( 1.68 \times 10^4 = 16,800 \)
- Now subtract:
- \( 429,000,000 - 16,800 = 428,983,200 \)
- **Final answer**: \( 4.289832 \times 10^8 \)

2. **\( 5.08 \times 10^{-4} - 3.12 \times 10^{-5} \)**
- Convert to standard form:
- \( 5.08 \times 10^{-4} = 0.000508 \)
- \( 3.12 \times 10^{-5} = 0.0000312 \)
- Now subtract:
- \( 0.000508 - 0.0000312 = 0.0004768 \)
- Convert back to scientific notation:
- \( 0.0004768 = 4.768 \times 10^{-4} \)
- **Final answer**: \( 4.768 \times 10^{-4} \)

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### Summary:
To correctly add or subtract decimals, always align them, use clear operational words, and ensure conversions are properly formatted for computations.