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Rewrite the following in scientific notation and calculate the answer in scientific notation. If necessary, convert your answer to scientific notation.

[tex]\[
\begin{array}{l}
0.000044 \div 0.00075
\end{array}
\][/tex]

[tex]\[ \square \][/tex]

(Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to one decimal place as needed.)


Sagot :

To solve the given problem, let's first rewrite the numbers 0.000044 and 0.00075 in scientific notation.

1. Rewrite the numbers in scientific notation:

The number [tex]\(0.000044\)[/tex] can be rewritten as [tex]\(4.4 \times 10^{-5}\)[/tex].

The number [tex]\(0.00075\)[/tex] can be rewritten as [tex]\(7.5 \times 10^{-4}\)[/tex].

2. Perform the division:

We need to divide [tex]\(4.4 \times 10^{-5}\)[/tex] by [tex]\(7.5 \times 10^{-4}\)[/tex]:

[tex]\[ \frac{4.4 \times 10^{-5}}{7.5 \times 10^{-4}} \][/tex]

3. Simplify the division:

To divide numbers in scientific notation, divide their coefficients and subtract the exponents:

[tex]\[ \frac{4.4}{7.5} \times 10^{-5 - (-4)} = \frac{4.4}{7.5} \times 10^{-5 + 4} = \frac{4.4}{7.5} \times 10^{-1} \][/tex]

4. Calculate the coefficient division:

Dividing the coefficients:

[tex]\[ \frac{4.4}{7.5} \approx 0.5866666666666667 \][/tex]

5. Combine the coefficient with the power of ten:

Thus, the result of the division in scientific notation is:

[tex]\[ 0.5866666666666667 \times 10^{-1} \][/tex]

6. Convert to proper scientific notation:

To express [tex]\(0.5866666666666667 \times 10^{-1}\)[/tex] in proper scientific notation, we move the decimal place one position to the right:

[tex]\[ 0.5866666666666667 \times 10^{-1} = 5.866666666666667 \times 10^{-2} \][/tex]

7. Round to one decimal place as needed:

Rounding [tex]\(5.866666666666667\)[/tex] to one decimal place gives [tex]\(5.9\)[/tex].

So, the final answer in scientific notation is:

[tex]\[ 5.9 \times 10^{-2} \][/tex]

Thus, the division of [tex]\(0.000044\)[/tex] by [tex]\(0.00075\)[/tex] in scientific notation is:

[tex]\[ \boxed{5.9 \times 10^{-2}} \][/tex]
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