QuestionCalculate $(2.5 \times 10^{-10})(7 \times 10^{-6})$ and express in scientific notation.

Studdy Solution

STEP 1

Assumptions1. We are multiplying two numbers in scientific notation. . The rules of multiplication and addition apply to the coefficients and exponents respectively.

STEP 2

First, we multiply the coefficients of the two numbers.
$Coefficient =2.5 \\times7$

STEP 3

Calculate the coefficient.
$Coefficient =2.5 \\times7 =17.5$

STEP 4

Next, we add the exponents of the two numbers.
$Exponent = -10 + -6$

STEP 5

Calculate the exponent.
$Exponent = -10 + - = -16$

STEP 6

Finally, we combine the coefficient and the exponent to express the answer in scientific notation.
$Answer = Coefficient \\times10^{Exponent}$

STEP 7

Plug in the values for the coefficient and the exponent to express the answer in scientific notation.
$Answer =17.5 \\times10^{-16}$ The correct answer is $1.75 \times10^{-15}$ .

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