QuestionDivide $3.525 \times 10^{10}$ by $4.7 \times 10^{-39}$ and express the result in scientific notation.

Studdy Solution

STEP 1

Assumptions1. We are dividing two numbers that are both in scientific notation. . The rules of division apply to scientific notation as they do to regular numbers.

STEP 2

We can divide numbers in scientific notation by dividing the coefficients (the numbers before the exponential part) and subtracting the exponents. $\left(a \times10^{m}\right) \div \left(b \times10^{n}\right) = \left(\frac{a}{b}\right) \times10^{m-n}$

STEP 3

Now, plug in the given values for the coefficients and exponents to calculate the quotient.
$\left(3.525 \times10^{10}\right) \div \left(.7 \times10^{-39}\right) = \left(\frac{3.525}{.7}\right) \times10^{10-(-39)}$

STEP 4

Calculate the division of the coefficients and the subtraction of the exponents.
$\left(\frac{3.525}{4.7}\right) \times10^{10-(-39)} =0.75 \times10^{49}$

STEP 5

The coefficient in scientific notation should be between1 and10. So, we need to adjust the coefficient and the exponent to fit this rule.
$0.75 \times10^{49} =7.5 \times10^{48}$ So, the quotient is $7.5 \times10^{48}$ .

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