Add Numbers in Scientific Notation with Different Powers
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 10: Exponents and Scientific Notation) learn to add numbers in scientific notation with different powers of 10 by first rewriting one number to match the other power, then adding the coefficients.
Key Concepts
To add numbers in scientific notation with different powers of 10, rewrite one number so both have the same power of 10, then add the coefficients: $(a \times 10^m) + (b \times 10^n) = (a' \times 10^k) + (b' \times 10^k) = (a' + b') \times 10^k$.
Common Questions
How do you add numbers in scientific notation with different powers?
Convert one number to match the other power of 10. Usually match the smaller power to the larger: adjust the coefficient and change the exponent. Then add the coefficients.
How do you add 3.2 x 10^5 and 4.7 x 10^4?
Rewrite 4.7 x 10^4 as 0.47 x 10^5. Then add: (3.2 + 0.47) x 10^5 = 3.67 x 10^5.
Why can you not directly add scientific notation numbers with different exponents?
Different powers of 10 represent different magnitudes. You must align them (like aligning decimal places) before adding coefficients.
What chapter in Big Ideas Math Advanced 2 covers adding scientific notation with different powers?
Chapter 10: Exponents and Scientific Notation in Big Ideas Math Advanced 2 (Grade 7) covers adding scientific notation with different powers.
Do you always match to the larger exponent?
You can match to either exponent. Matching to the larger is typical because it avoids very small coefficients, but either approach gives the correct answer.