High School

Express in scientific notation. Choose the answer with the proper number of significant figures.

[tex]$69,000,000,000 =$[/tex]

A. [tex]$6.9 \times 10^{10}$[/tex]

B. [tex]$6.9^{10}$[/tex]

C. [tex]$69 \times 10^9$[/tex]

Answer :

We start by writing the number as a product of a decimal number between 1 and 10 (the mantissa) and a power of 10.

1. Write the number 69,000,000,000 as a decimal with one digit to the left of the decimal point. Moving the decimal point 10 places to the left, we obtain

[tex]$$6.9 \times 10^{10}.$$[/tex]

2. Notice that in the original number, only the digits 6 and 9 are significant. Therefore, the mantissa must have two significant figures, which is why [tex]$6.9$[/tex] is used.

Thus, the expression in scientific notation with the proper number of significant figures is

[tex]$$6.9 \times 10^{10}.$$[/tex]