Section 10.7: Operations in Scientific Notation

Property

When adding numbers in scientific notation with the same power of 10, use the distributive property:

Examples

Property

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: $(a \times 10^m) + (b \times 10^n) = (a' \times 10^k) + (b' \times 10^k) = (a' + b') \times 10^k$

Examples

Property

When subtracting numbers in scientific notation with the same power of 10, subtract the coefficients and keep the same power: $(a \times 10^n) - (b \times 10^n) = (a - b) \times 10^n$

Examples

Property

To subtract numbers in scientific notation with different powers of 10, first rewrite one number so both have the same power of 10, then subtract the coefficients: $(a \times 10^m) - (b \times 10^n) = (a \times 10^{m-n} - b) \times 10^n$ when $m > n$, or $(a - b \times 10^{n-m}) \times 10^m$ when $n > m$.

Examples