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QuestionCalculate (2.72×10−5)(3.11×109)(1.99×103)(2.44×10−11)\frac{\left(2.72 \times 10^{-5}\right)\left(3.11 \times 10^{9}\right)}{\left(1.99 \times 10^{3}\right)\left(2.44 \times 10^{-11}\right)}.

Studdy Solution

STEP 1

Assumptions1. We are dealing with numbers in scientific notation. . The operation to be performed is division.
3. The order of operations must be followed, which is multiplication before division.

STEP 2

First, we need to perform the multiplication operations in the numerator and the denominator separately.
umerator=(2.72×10−5)(.11×109)umerator = \left(2.72 \times10^{-5}\right)\left(.11 \times10^{9}\right)Denominator=(1.99×10)(2.44×10−11)Denominator = \left(1.99 \times10^{}\right)\left(2.44 \times10^{-11}\right)

STEP 3

When multiplying numbers in scientific notation, we multiply the coefficients and add the exponents.
umerator=2.72×3.11×10−5+9umerator =2.72 \times3.11 \times10^{-5+9}Denominator=1.99×2.44×103−11Denominator =1.99 \times2.44 \times10^{3-11}

STEP 4

Perform the multiplication of the coefficients and the addition of the exponents.
umerator=8.4572×104umerator =8.4572 \times10^{4}Denominator=4.8576×10−8Denominator =4.8576 \times10^{-8}

STEP 5

Now, we need to perform the division operation. When dividing numbers in scientific notation, we divide the coefficients and subtract the exponents.
umeratorDenominator=8.45724.857×104−(−8)\frac{umerator}{Denominator} = \frac{8.4572}{4.857} \times10^{4-(-8)}

STEP 6

Perform the division of the coefficients and the subtraction of the exponents.
umeratorDenominator=1.74×1012\frac{umerator}{Denominator} =1.74 \times10^{12}The solution to the problem is 1.74×10121.74 \times10^{12}.

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