Question

add numbers in scientific notation practice and quick check

Answer 1

Sure! Here's a quick guide on how to add numbers in scientific notation, followed by some practice problems and a quick check.

### How to Add Numbers in Scientific Notation

1. **Ensure the Powers of 10 are the Same**: If the exponents are different, you'll need to adjust them so that they are the same. This often means converting one number to have the same exponent as the other.

2. **Add the Coefficients**: Once the powers of 10 are the same, you can add the coefficients directly.

3. **Adjust if Necessary**: If the resulting coefficient is 10 or greater, you should adjust it back into scientific notation by increasing the exponent by 1.

### Example:

Suppose you have the following numbers:
\( 3.2 \times 10^4 + 4.8 \times 10^5 \)

1. Convert \( 3.2 \times 10^4 \) to have the same exponent as \( 4.8 \times 10^5 \):
\( 3.2 \times 10^4 = 0.032 \times 10^5 \)

2. Now add the coefficients:
\( 0.032 + 4.8 = 4.832 \)

3. Write it in scientific notation:
\( 4.832 \times 10^5 \)

### Practice Problems

Now try adding the following pairs of numbers in scientific notation:

1. \( 2.5 \times 10^3 + 3.4 \times 10^3 \)
2. \( 5.0 \times 10^{10} + 2.1 \times 10^{9} \)
3. \( 7.2 \times 10^{-6} + 1.3 \times 10^{-7} \)
4. \( 4.0 \times 10^{2} + 1.5 \times 10^{3} \)
5. \( 6.3 \times 10^{8} + 4.5 \times 10^{7} \)

### Quick Check Answers

1. **Problem**: \( 2.5 \times 10^3 + 3.4 \times 10^3 \)
**Answer**: \( 5.9 \times 10^3 \)

2. **Problem**: \( 5.0 \times 10^{10} + 2.1 \times 10^{9} \)
**Answer**: \( 5.21 \times 10^{10} \)

3. **Problem**: \( 7.2 \times 10^{-6} + 1.3 \times 10^{-7} \)
**Answer**: \( 7.33 \times 10^{-6} \) (after converting \( 1.3 \times 10^{-7} \) to \( 0.13 \times 10^{-6} \))

4. **Problem**: \( 4.0 \times 10^{2} + 1.5 \times 10^{3} \)
**Answer**: \( 1.9 \times 10^{3} \)

5. **Problem**: \( 6.3 \times 10^{8} + 4.5 \times 10^{7} \)
**Answer**: \( 6.75 \times 10^{8} \) (after converting \( 4.5 \times 10^{7} \) to \( 0.45 \times 10^{8} \))

Feel free to reach out if you have more questions or need further clarification!