Adding and subtracting scientific notation worksheet: Fill out ... - Free Printable

Problem: Solve the given problems involving addition and subtraction of numbers in scientific notation.

#### Steps to Solve:
1. Understand Scientific Notation: Numbers in scientific notation are written as \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.
2. Align Exponents: To add or subtract numbers in scientific notation, the exponents must be the same. If they are different, adjust one or both numbers so that their exponents match.
3. Perform Addition/Subtraction: Add or subtract the coefficients (the \( a \) values) while keeping the exponent the same.
4. Simplify if Necessary: Ensure the result is in proper scientific notation (\( 1 \leq a < 10 \)).

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Solutions:

#### Problem 1: \( 1.9 \times 10^3 + 2.3 \times 10^4 \)
- Align exponents:
- Rewrite \( 1.9 \times 10^3 \) as \( 0.19 \times 10^4 \).
- Add the coefficients:
\[
0.19 \times 10^4 + 2.3 \times 10^4 = (0.19 + 2.3) \times 10^4 = 2.49 \times 10^4
\]
- Answer: \( 2.49 \times 10^4 \)

#### Problem 2: \( 1.5 \times 10^2 + 5.2 \times 10^5 \)
- Align exponents:
- Rewrite \( 1.5 \times 10^2 \) as \( 0.00015 \times 10^5 \).
- Add the coefficients:
\[
0.00015 \times 10^5 + 5.2 \times 10^5 = (0.00015 + 5.2) \times 10^5 = 5.20015 \times 10^5
\]
- Answer: \( 5.20015 \times 10^5 \)

#### Problem 3: \( 1.0 \times 10^4 + 2.8 \times 10^6 \)
- Align exponents:
- Rewrite \( 1.0 \times 10^4 \) as \( 0.0001 \times 10^6 \).
- Add the coefficients:
\[
0.0001 \times 10^6 + 2.8 \times 10^6 = (0.0001 + 2.8) \times 10^6 = 2.8001 \times 10^6
\]
- Answer: \( 2.8001 \times 10^6 \)

#### Problem 4: \( 7.7 \times 10^3 + 8.6 \times 10^4 \)
- Align exponents:
- Rewrite \( 7.7 \times 10^3 \) as \( 0.77 \times 10^4 \).
- Add the coefficients:
\[
0.77 \times 10^4 + 8.6 \times 10^4 = (0.77 + 8.6) \times 10^4 = 9.37 \times 10^4
\]
- Answer: \( 9.37 \times 10^4 \)

#### Problem 5: \( 3.3 \times 10^4 + 14.5 \times 10^5 \)
- Align exponents:
- Rewrite \( 3.3 \times 10^4 \) as \( 0.033 \times 10^5 \).
- Add the coefficients:
\[
0.033 \times 10^5 + 14.5 \times 10^5 = (0.033 + 14.5) \times 10^5 = 14.533 \times 10^5
\]
- Answer: \( 14.533 \times 10^5 \) (or \( 1.4533 \times 10^6 \) if normalized)

#### Problem 6: \( 8.8 \times 10^4 - 2.7 \times 10^2 \)
- Align exponents:
- Rewrite \( 2.7 \times 10^2 \) as \( 0.0027 \times 10^4 \).
- Subtract the coefficients:
\[
8.8 \times 10^4 - 0.0027 \times 10^4 = (8.8 - 0.0027) \times 10^4 = 8.7973 \times 10^4
\]
- Answer: \( 8.7973 \times 10^4 \)

#### Problem 7: \( 7.5 \times 10^3 - 8.9 \times 10^4 \)
- Align exponents:
- Rewrite \( 7.5 \times 10^3 \) as \( 0.075 \times 10^4 \).
- Subtract the coefficients:
\[
0.075 \times 10^4 - 8.9 \times 10^4 = (0.075 - 8.9) \times 10^4 = -8.825 \times 10^4
\]
- Answer: \( -8.825 \times 10^4 \)

#### Problem 8: \( 8.7 \times 10^3 - 8.20 \times 10^2 \)
- Align exponents:
- Rewrite \( 8.20 \times 10^2 \) as \( 0.82 \times 10^3 \).
- Subtract the coefficients:
\[
8.7 \times 10^3 - 0.82 \times 10^3 = (8.7 - 0.82) \times 10^3 = 7.88 \times 10^3
\]
- Answer: \( 7.88 \times 10^3 \)

#### Problem 9: \( 9.9 \times 10^2 - 5.54 \times 10^4 \)
- Align exponents:
- Rewrite \( 9.9 \times 10^2 \) as \( 0.099 \times 10^4 \).
- Subtract the coefficients:
\[
0.099 \times 10^4 - 5.54 \times 10^4 = (0.099 - 5.54) \times 10^4 = -5.441 \times 10^4
\]
- Answer: \( -5.441 \times 10^4 \)

#### Problem 10: \( 10 \times 10^2 - 7.79 \times 10^3 \)
- Align exponents:
- Rewrite \( 10 \times 10^2 \) as \( 1 \times 10^3 \).
- Subtract the coefficients:
\[
1 \times 10^3 - 7.79 \times 10^3 = (1 - 7.79) \times 10^3 = -6.79 \times 10^3
\]
- Answer: \( -6.79 \times 10^3 \)

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Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 2.49 \times 10^4 \\
2. & \ 5.20015 \times 10^5 \\
3. & \ 2.8001 \times 10^6 \\
4. & \ 9.37 \times 10^4 \\
5. & \ 14.533 \times 10^5 \\
6. & \ 8.7973 \times 10^4 \\
7. & \ -8.825 \times 10^4 \\
8. & \ 7.88 \times 10^3 \\
9. & \ -5.441 \times 10^4 \\
10. & \ -6.79 \times 10^3
\end{aligned}
}
\]