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
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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.
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Add the Coefficients: Once the powers of 10 are the same, you can add the coefficients directly.
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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:
\( 3.2 \times 10^4 + 4.8 \times 10^5 \)
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Convert \( 3.2 \times 10^4 \) to have the same exponent as \( 4.8 \times 10^5 \):
\( 3.2 \times 10^4 = 0.032 \times 10^5 \) -
Now add the coefficients:
\( 0.032 + 4.8 = 4.832 \) -
Write it in scientific notation:
\( 4.832 \times 10^5 \)
Practice Problems
Now try adding the following pairs of numbers in scientific notation:
- \( 2.5 \times 10^3 + 3.4 \times 10^3 \)
- \( 5.0 \times 10^{10} + 2.1 \times 10^{9} \)
- \( 7.2 \times 10^{-6} + 1.3 \times 10^{-7} \)
- \( 4.0 \times 10^{2} + 1.5 \times 10^{3} \)
- \( 6.3 \times 10^{8} + 4.5 \times 10^{7} \)
Quick Check Answers
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Problem: \( 2.5 \times 10^3 + 3.4 \times 10^3 \)
Answer: \( 5.9 \times 10^3 \) -
Problem: \( 5.0 \times 10^{10} + 2.1 \times 10^{9} \)
Answer: \( 5.21 \times 10^{10} \) -
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 \( 0.13 \times 10^{-6} \)) -
Problem: \( 4.0 \times 10^{2} + 1.5 \times 10^{3} \)
Answer: \( 1.9 \times 10^{3} \) -
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!
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