To subtract numbers in scientific notation, you first need to ensure that the numbers have the same exponent. Here’s a step-by-step guide on how to do this:
Step 1: Write the Numbers in Scientific Notation
For example, let's say you want to subtract \( 4.5 \times 10^6 \) from \( 2.1 \times 10^7 \).
Step 2: Adjust the Exponents
Make sure both numbers have the same exponent. In this case, we can convert \( 2.1 \times 10^7 \) to the same exponent as \( 4.5 \times 10^6 \):
\[ 2.1 \times 10^7 = 21.0 \times 10^6 \]
Step 3: Perform the Subtraction
Now that both numbers have the same exponent, you can subtract them:
\[ 21.0 \times 10^6 - 4.5 \times 10^6 = (21.0 - 4.5) \times 10^6 = 16.5 \times 10^6 \]
Step 4: Simplify (if necessary)
Finally, you can express it in standard scientific notation form. In this case, \( 16.5 \times 10^6 \) is already in scientific notation.
Final Answer
Thus,
\[ 2.1 \times 10^7 - 4.5 \times 10^6 = 16.5 \times 10^6 \]
Example
Let’s do another example:
Subtract \( 3.2 \times 10^5 \) from \( 1.5 \times 10^6 \).
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Write down the numbers: \[ 1.5 \times 10^6, \quad 3.2 \times 10^5 \]
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Adjust the exponent of \( 1.5 \times 10^6 \): \[ 3.2 \times 10^5 = 0.32 \times 10^6 \]
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Now perform the subtraction: \[ 1.5 \times 10^6 - 0.32 \times 10^6 = (1.5 - 0.32) \times 10^6 = 1.18 \times 10^6 \]
Final Answer
So,
\[ 1.5 \times 10^6 - 3.2 \times 10^5 = 1.18 \times 10^6 \]
This method can be applied to any subtraction problem involving numbers in scientific notation.
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