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QuestionCalculate the decimal value of 8.4×10−74×10−4\frac{8.4 \times 10^{-7}}{4 \times 10^{-4}}.

Studdy Solution

STEP 1

Assumptions1. The numerator is 8.4×10−78.4 \times10^{-7} . The denominator is 4×10−44 \times10^{-4}
3. We need to perform the division operation and express the answer in decimal notation.

STEP 2

First, we can simplify the division by separating the numerical part and the power of10 part.
8.4×10−74×10−4=8.44×10−710−4\frac{8.4 \times10^{-7}}{4 \times10^{-4}} = \frac{8.4}{4} \times \frac{10^{-7}}{10^{-4}}

STEP 3

Perform the division of the numerical part.
8.=2.1\frac{8.}{} =2.1

STEP 4

For the power of10 part, remember that when you divide two exponents with the same base, you subtract the exponents.
10−710−4=10−7−(−4)=10−3\frac{10^{-7}}{10^{-4}} =10^{-7 - (-4)} =10^{-3}

STEP 5

Now, multiply the results from step3 and step4.
2.1×10−32.1 \times10^{-3}

STEP 6

Express the result in decimal notation.
2.1×10−3=0.00212.1 \times10^{-3} =0.0021So, the result of the operation is0.0021.

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