Sure! In a typical unit focused on subtracting numbers in scientific notation, you may be required to complete the following steps to solve problems effectively. Here’s a structured approach to help you with a quick check or review:
Steps to Subtract Numbers in Scientific Notation:
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Ensure Exponents are the Same: The first step in subtracting numbers in scientific notation is to ensure that the numbers have the same exponent. If they don’t, you will need to adjust one of the numbers so that both have the same exponent.
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Convert If Necessary: If the exponents are different, convert one of the numbers. For instance:
- Convert \( a \times 10^m \) to \( a \times 10^n \) by adjusting the coefficient (
a) such that it equals \( a \times 10^{m-n} \times 10^n \) if you are changing \( 10^m \) to \( 10^n \).
- Convert \( a \times 10^m \) to \( a \times 10^n \) by adjusting the coefficient (
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Perform the Subtraction: After converting (if necessary) so both numbers have the same exponent, you can directly subtract the coefficients: \[ (a \times 10^n) - (b \times 10^n) = (a - b) \times 10^n \]
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Write Your Answer: If needed, write the result in scientific notation. If the coefficient is not between 1 and 10 after subtraction, adjust it back into proper scientific notation.
Example:
Subtract \( 4.5 \times 10^3 \) from \( 2.3 \times 10^4 \).
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Ensure same exponent:
Convert \( 2.3 \times 10^4 \) to have an exponent of 3:
\[ 2.3 \times 10^4 = 23 \times 10^3 \] -
Now we have:
\( 23 \times 10^3 - 4.5 \times 10^3 \) -
Perform the subtraction:
\[ (23 - 4.5) \times 10^3 = 18.5 \times 10^3 \] -
Convert to proper scientific notation if necessary:
\( 18.5 \times 10^3 = 1.85 \times 10^4 \) (since \( 18.5 = 1.85 \times 10^1 \))
Final Answer:
\[ 1.85 \times 10^4 \]
Feel free to ask if you have specific questions or examples you'd like to work through!
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