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QuestionCalculate (9.7×108)⋅(4×10−6)(9.7 \times 10^{8}) \cdot (4 \times 10^{-6}) and give the answer in decimal form.

Studdy Solution

STEP 1

Assumptions1. We are given two numbers in scientific notation 9.7×1089.7 \times10^{8} and 4×10−64 \times10^{-6}. . We are asked to multiply these two numbers and express the answer in decimal notation.

STEP 2

In order to multiply these two numbers, we can use the properties of exponents. Specifically, when we multiply two numbers with the same base, we can add the exponents.The general rule is am⋅an=am+na^{m} \cdot a^{n} = a^{m+n}

STEP 3

Apply the rule to our problem. We can separate the multiplication into two parts the multiplication of the decimal parts (9.7 and) and the multiplication of the exponential parts (10810^{8} and 10−610^{-6}).
(9.7×108)⋅(×10−6)=(9.7⋅)×(108⋅10−6)\left(9.7 \times10^{8}\right) \cdot\left( \times10^{-6}\right) = (9.7 \cdot) \times (10^{8} \cdot10^{-6})

STEP 4

Calculate the multiplication of the decimal parts.
9.7⋅4=38.89.7 \cdot4 =38.8

STEP 5

Calculate the multiplication of the exponential parts by adding the exponents.
108⋅10−=108+(−)=10210^{8} \cdot10^{-} =10^{8 + (-)} =10^{2}

STEP 6

Combine the results from steps4 and5.
(9.⋅4)×(108⋅10−6)=38.8×102(9. \cdot4) \times (10^{8} \cdot10^{-6}) =38.8 \times10^{2}

STEP 7

Finally, express the result in decimal notation. 10210^{2} means we move the decimal point two places to the right.
38.×102=388038. \times10^{2} =3880So, the result of the operation (9.7×10)⋅(4×10−6)\left(9.7 \times10^{}\right) \cdot\left(4 \times10^{-6}\right) is3880.

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