Subtract. Write your answer in scientific notation. (2 x 10^5) - (8.3 x 10^3)

Understand the Problem

The question is asking us to subtract two numbers in scientific notation and provide the answer in the same format. We need to convert, if necessary, and align the exponents before performing the subtraction.

Answer

$1.917 \times 10^5$

Steps to Solve

Identify the terms
We have two numbers in scientific notation: $2 \times 10^5$ and $8.3 \times 10^3$.
Align the exponents
To subtract these numbers, we need to have the same exponent. We can convert $8.3 \times 10^3$ to base $10^5$:
- $8.3 \times 10^3 = 0.083 \times 10^5$
Perform the subtraction
Now that both terms are in the same format, we can subtract:

$$ (2 \times 10^5) - (0.083 \times 10^5) = (2 - 0.083) \times 10^5 $$
- Calculate:
  $$ 2 - 0.083 = 1.917 $$
Express the final answer
Now, we write the result in scientific notation:
$$ 1.917 \times 10^5 $$

The final answer is $1.917 \times 10^5$.

More Information

The subtraction was done by aligning the exponents and converting one of the terms to have the same base. This allows for straightforward subtraction while maintaining the scientific notation format.

Tips

Converting the numbers incorrectly when aligning the exponents. Always ensure the exponent base matches before performing operations.

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