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QuestionCalculate the product of 1.08×10−31.08 \times 10^{-3} and 9.3×10−39.3 \times 10^{-3}.

Studdy Solution

STEP 1

Assumptions1. We are multiplying two numbers in scientific notation. . The rules of multiplication apply as usual, but we need to handle the powers of10 separately.

STEP 2

First, we multiply the coefficients (the numbers before the powers of10).
Coefficient=1.08×9.Coefficient =1.08 \times9.

STEP 3

Calculate the value of the coefficient.
Coefficient=1.08×9.3=10.044Coefficient =1.08 \times9.3 =10.044

STEP 4

Next, we multiply the powers of10 together. When multiplying powers of10, we add the exponents.
Power of 10=10−3×10−3=10−3−3Power\, of\,10 =10^{-3} \times10^{-3} =10^{-3-3}

STEP 5

Calculate the value of the power of10.
Power of 10=10−3−3=10−Power\, of\,10 =10^{-3-3} =10^{-}

STEP 6

Finally, we multiply the coefficient and the power of10 together to get the final answer.
Answer=Coefficient×Power of 10Answer = Coefficient \times Power\, of\,10

STEP 7

Plug in the values for the coefficient and the power of10 to calculate the answer.
Answer=10.044×10−6Answer =10.044 \times10^{-6}

STEP 8

Calculate the final answer.
Answer=10.044×10−6=1.0044×10−2Answer =10.044 \times10^{-6} =1.0044 \times10^{-2}So, (1.08×10−3)(.3×10−3)=1.0044×10−2\left(1.08 \times10^{-3}\right)\left(.3 \times10^{-3}\right) =1.0044 \times10^{-2}.

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