Math

QuestionCalculate the product: (3.5×108)(5×103)=(3.5 \times 10^{8}) \cdot (5 \times 10^{-3}) =

Studdy Solution

STEP 1

Assumptions1. We are multiplying two numbers in scientific notation. . The rules of multiplication and exponentiation apply.

STEP 2

We start by multiplying the coefficients (the numbers before the exponentiation).
Coefficient=.5×5Coefficient =.5 \times5

STEP 3

Calculate the coefficient.
Coefficient=3.5×5=17.5Coefficient =3.5 \times5 =17.5

STEP 4

Next, we multiply the powers of10 together. When multiplying numbers in scientific notation, we add the exponents.
Powerof10=108×103=108+(3)Power\, of\,10 =10^{8} \times10^{-3} =10^{8 + (-3)}

STEP 5

Calculate the power of10.
Powerof10=108+(3)=105Power\, of\,10 =10^{8 + (-3)} =10^{5}

STEP 6

Now, we put the coefficient and the power of10 together to get the answer.
Answer=Coefficient×Powerof10Answer = Coefficient \times Power\, of\,10

STEP 7

Plug in the values for the coefficient and the power of10 to get the answer.
Answer=17.5×105Answer =17.5 \times10^{5}The answer to (3.5×10)(5×103)\left(3.5 \times10^{}\right) \cdot\left(5 \times10^{-3}\right) is 17.5×10517.5 \times10^{5}.

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