Answer :
To express a number in scientific notation, we want it in the form
[tex]$$
a \times 10^n,
$$[/tex]
where [tex]$1 \leq a < 10$[/tex] and the exponent [tex]$n$[/tex] is an integer.
We start with the number
[tex]$$
93,\!000,\!000.
$$[/tex]
1. The first step is to rewrite the number so that only one nonzero digit appears before the decimal point. We do this by moving the decimal point to the left. Moving it 7 places to the left gives:
[tex]$$
93,\!000,\!000 = 9.3 \times 10^7.
$$[/tex]
2. Here, [tex]$9.3$[/tex] is the mantissa (which satisfies [tex]$1 \leq a < 10$[/tex]) and [tex]$7$[/tex] is the exponent of [tex]$10$[/tex]. This shows that we have shifted the decimal point 7 places.
Thus, the number [tex]$93,\!000,\!000$[/tex] in scientific notation is
[tex]$$
9.3 \times 10^7.
$$[/tex]
This corresponds to option (c).
[tex]$$
a \times 10^n,
$$[/tex]
where [tex]$1 \leq a < 10$[/tex] and the exponent [tex]$n$[/tex] is an integer.
We start with the number
[tex]$$
93,\!000,\!000.
$$[/tex]
1. The first step is to rewrite the number so that only one nonzero digit appears before the decimal point. We do this by moving the decimal point to the left. Moving it 7 places to the left gives:
[tex]$$
93,\!000,\!000 = 9.3 \times 10^7.
$$[/tex]
2. Here, [tex]$9.3$[/tex] is the mantissa (which satisfies [tex]$1 \leq a < 10$[/tex]) and [tex]$7$[/tex] is the exponent of [tex]$10$[/tex]. This shows that we have shifted the decimal point 7 places.
Thus, the number [tex]$93,\!000,\!000$[/tex] in scientific notation is
[tex]$$
9.3 \times 10^7.
$$[/tex]
This corresponds to option (c).
