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What is the product of 700 and 180,000 written in scientific notation?

A. [tex]12.6 \times 10^9[/tex]
B. [tex]126 \times 10^9[/tex]
C. [tex]126 \times 10^9[/tex]
D. [tex]126 \times 10^{10}[/tex]
E. [tex]126,000,000[/tex]

Answer :

To solve the problem, we begin by multiplying the two numbers:

[tex]$$700 \times 180\,000 = 126\,000\,000.$$[/tex]

Next, we write this result in scientific notation. Scientific notation expresses a number in the form

[tex]$$a \times 10^n,$$[/tex]

where [tex]\(a\)[/tex] is a number between 1 and 10 and [tex]\(n\)[/tex] is an integer.

To convert [tex]\(126\,000\,000\)[/tex] into this form, we move the decimal point in [tex]\(126\,000\,000\)[/tex] so that there is one digit to the left of the decimal. Moving the decimal point 8 places to the left, we have:

[tex]$$126\,000\,000 = 1.26 \times 10^8.$$[/tex]

Thus, the product of 700 and 180,000 written in scientific notation is

[tex]$$\boxed{1.26 \times 10^8}.$$[/tex]

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