Subtract in Scientific Notation
To subtract numbers in scientific notation, the powers of 10 must be the same. The subtraction is performed using the distributive property: . If the powers are different, first rewrite one of the numbers so the exponents match. This concept is part of Big Ideas Math, Course 2, Accelerated for Grade 7 students, covered in Chapter 6: Exponents and Scientific Notation.
Key Concepts
Property To subtract numbers in scientific notation, the powers of 10 must be the same. The subtraction is performed using the distributive property: $(a \times 10^n) (b \times 10^n) = (a b) \times 10^n$. If the powers are different, first rewrite one of the numbers so the exponents match.
Examples Same powers: $(8.5 \times 10^4) (2.1 \times 10^4) = (8.5 2.1) \times 10^4 = 6.4 \times 10^4$ Different powers: $(7.2 \times 10^5) (4.1 \times 10^3) = (7.2 \times 10^5) (0.041 \times 10^5) = (7.2 0.041) \times 10^5 = 7.159 \times 10^5$.
Explanation When subtracting numbers in scientific notation, you must ensure the exponents on the powers of 10 are identical. If they are, simply subtract the decimal factors and keep the same power of 10. If the exponents are different, you must adjust one of the numbers by moving its decimal point and changing its exponent until the exponents match. After matching the exponents, you can proceed with the subtraction.
Common Questions
What is Subtract in Scientific Notation in accelerated middle school math?
To subtract numbers in scientific notation, the powers of 10 must be the same. The subtraction is performed using the distributive property: .
What is the formula or rule for Subtract in Scientific Notation?
The key mathematical expression for Subtract in Scientific Notation is: (a \times 10^n) - (b \times 10^n) = (a - b) \times 10^n. Students apply this rule when solving accelerated middle school math problems.
Why is Subtract in Scientific Notation an important concept in Grade 7 math?
Subtract in Scientific Notation builds foundational skills in accelerated middle school math. Mastering this concept prepares students for more complex equations and higher-level mathematics within Chapter 6: Exponents and Scientific Notation.
What grade level is Subtract in Scientific Notation taught at?
Subtract in Scientific Notation is taught at the Grade 7 level in California using Big Ideas Math, Course 2, Accelerated. It is part of the Chapter 6: Exponents and Scientific Notation unit.
Where is Subtract in Scientific Notation covered in the textbook?
Subtract in Scientific Notation appears in Big Ideas Math, Course 2, Accelerated, Chapter 6: Exponents and Scientific Notation. This is a Grade 7 course following California math standards.