QuestionCalculate $6.2 \times 10^{-13} \times 5.68 \times 10^{8}$ and report the answer with the correct significant figures.

Studdy Solution

STEP 1

Assumptions1. The multiplication operation is between two numbers in scientific notation. . The result should be reported to the correct number of significant figures.

STEP 2

First, we need to multiply the significant figures (also known as mantissas) of the two numbers.
$Mantissa\, product =6.2 \\times5.68$

STEP 3

Calculate the product of the mantissas.
$Mantissa\, product =6.2 \\times5.68 =35.216$

STEP 4

Next, we need to add the exponents of the two numbers.
$Exponent\, sum = -13 +8$

STEP 5

Calculate the sum of the exponents.
$Exponent\, sum = -13 +8 = -5$

STEP 6

Combine the mantissa product and the exponent sum to form the result in scientific notation.
$Result = Mantissa\, product \\times10^{Exponent\, sum}$

STEP 7

Plug in the values for the mantissa product and the exponent sum to calculate the result.
$Result =35.216 \\times10^{-5}$

STEP 8

The result in scientific notation should have the form of a single digit before the decimal point followed by the remaining digits. So, we need to adjust the mantissa and the exponent to fit this form.
$Adjusted\, result =3.5216 \\times10^{-4}$

STEP 9

The number of significant figures in the result should be determined by the number with the least significant figures in the original problem. In this case, the number6.2 has the least significant figures (2). So, the result should also have2 significant figures.
$Final\, result =3.5 \\times^{-4}$ The result of the multiplication operation to the correct number of significant figures is $3.5 \times^{-4}$ .

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