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QuestionCompute and express in decimal: (2×108)(2×10−5)=□(2 \times 10^{8})(2 \times 10^{-5}) = \square (Type an integer or decimal.)

Studdy Solution

STEP 1

Assumptions1. We are multiplying two numbers in scientific notation. . The base of the exponent in the scientific notation is10.

STEP 2

When multiplying numbers in scientific notation, we can separate the multiplication into two parts the multiplication of the numbers and the multiplication of the powers of10.
(2×108)(2×10−5)=(2×2)×(108×10−5)\left(2 \times10^{8}\right)\left(2 \times10^{-5}\right) = (2 \times2) \times (10^{8} \times10^{-5})

STEP 3

Calculate the multiplication of the numbers.
2×2=2 \times2 =

STEP 4

For the multiplication of the powers of10, we add the exponents.
108×10−=108+(−)=10310^{8} \times10^{-} =10^{8 + (-)} =10^{3}

STEP 5

Combine the results from steps3 and4 to get the final answer.
(2×2)×(108×10−5)=4×103(2 \times2) \times (10^{8} \times10^{-5}) =4 \times10^{3}

STEP 6

Express the answer in decimal notation.
4×103=40004 \times10^{3} =4000The answer is4000.

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