Subtract Numbers in Scientific Notation with Different Powers
Subtract Numbers in Scientific Notation with Different Powers is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 10: Exponents and Scientific Notation, where students adjust one number so both share the same power of 10 before subtracting, ensuring the coefficients can be combined while keeping the result in proper scientific notation. This is the most challenging operation with scientific notation.
Key Concepts
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 $n m$.
Common Questions
How do you subtract numbers in scientific notation with different powers?
Convert one number so both have the same power of 10 by adjusting its coefficient. Then subtract the coefficients and keep the common power of 10. Check that the result is in proper scientific notation (coefficient between 1 and 10).
What does it mean to adjust the coefficient in scientific notation?
To increase the exponent by 1, move the decimal point in the coefficient one place to the left (dividing the coefficient by 10). To decrease the exponent by 1, move the decimal right (multiplying by 10). The value of the number stays the same.
What is an example of subtracting scientific notation with different powers?
5.2 x 10^6 - 3.0 x 10^5: convert 3.0 x 10^5 to 0.30 x 10^6. Then compute (5.2 - 0.30) x 10^6 = 4.9 x 10^6.
What is Big Ideas Math Advanced 2 Chapter 10 about?
Chapter 10 covers Exponents and Scientific Notation, including exponent rules, writing numbers in scientific notation, and performing all four operations with numbers in scientific notation.