Answer :
We want to express the number 591,000 in scientific notation. The key idea is to write the number in the form
[tex]$$
a \times 10^n
$$[/tex]
where [tex]$1 \leq a < 10$[/tex] and [tex]$n$[/tex] is an integer.
Here’s the step-by-step process:
1. Start with 591,000. We need to move the decimal point so that only one nonzero digit is to its left. Starting from
[tex]$$
591000 = 591000.0,
$$[/tex]
we move the decimal point 5 places to the left, giving
[tex]$$
5.91.
$$[/tex]
2. To keep the value of the original number, we multiply by [tex]$10^5$[/tex], since the decimal was moved 5 places. So, we write
[tex]$$
5.91 \times 10^5.
$$[/tex]
3. Compare this with the provided options:
- Option a: [tex]$591 \times 10^4$[/tex] evaluates to [tex]$591 \times 10000 = 5,910,000$[/tex], which is too large.
- Option b: [tex]$5.91 \times 10^5$[/tex] evaluates to [tex]$5.91 \times 100000 = 591,000$[/tex], which exactly matches the area.
- Option c: [tex]$59.1 \times 10^5$[/tex] evaluates to [tex]$59.1 \times 100000 = 5,910,000$[/tex], which is incorrect.
- Option d: [tex]$5.91 \times 10^6$[/tex] evaluates to [tex]$5.91 \times 1000000 = 5,910,000$[/tex], which is also incorrect.
Since only option b yields the correct value of 591,000, we conclude that
[tex]$$
\textbf{Answer: } 5.91 \times 10^5.
$$[/tex]
[tex]$$
a \times 10^n
$$[/tex]
where [tex]$1 \leq a < 10$[/tex] and [tex]$n$[/tex] is an integer.
Here’s the step-by-step process:
1. Start with 591,000. We need to move the decimal point so that only one nonzero digit is to its left. Starting from
[tex]$$
591000 = 591000.0,
$$[/tex]
we move the decimal point 5 places to the left, giving
[tex]$$
5.91.
$$[/tex]
2. To keep the value of the original number, we multiply by [tex]$10^5$[/tex], since the decimal was moved 5 places. So, we write
[tex]$$
5.91 \times 10^5.
$$[/tex]
3. Compare this with the provided options:
- Option a: [tex]$591 \times 10^4$[/tex] evaluates to [tex]$591 \times 10000 = 5,910,000$[/tex], which is too large.
- Option b: [tex]$5.91 \times 10^5$[/tex] evaluates to [tex]$5.91 \times 100000 = 591,000$[/tex], which exactly matches the area.
- Option c: [tex]$59.1 \times 10^5$[/tex] evaluates to [tex]$59.1 \times 100000 = 5,910,000$[/tex], which is incorrect.
- Option d: [tex]$5.91 \times 10^6$[/tex] evaluates to [tex]$5.91 \times 1000000 = 5,910,000$[/tex], which is also incorrect.
Since only option b yields the correct value of 591,000, we conclude that
[tex]$$
\textbf{Answer: } 5.91 \times 10^5.
$$[/tex]
