College

What is [tex]$93,000,000$[/tex] written in scientific notation?

A. [tex]93 \times 10^6[/tex]
B. [tex]93 \times 10^7[/tex]
C. [tex]9.3 \times 10^7[/tex]
D. [tex]9.3 \times 10^6[/tex]

Answer :

To express [tex]$93,\!000,\!000$[/tex] in scientific notation, we want a number in the form

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

where [tex]$1 \leq a < 10$[/tex] and [tex]$n$[/tex] is an integer.

1. Start with the number [tex]$93,\!000,\!000$[/tex].
2. To have the significand between 1 and 10, move the decimal point so that only one nonzero digit is to the left of the decimal. Moving the decimal point 7 places to the left turns [tex]$93,\!000,\!000$[/tex] into [tex]$9.3$[/tex].
3. Since we moved the decimal 7 places, we multiply by [tex]$10^7$[/tex]. This gives us the scientific notation:

[tex]$$
9.3 \times 10^7.
$$[/tex]

Thus, the scientific notation for [tex]$93,\!000,\!000$[/tex] is

[tex]$$
9.3 \times 10^7.
$$[/tex]