Let's determine the correct standard form of 165,000.
Step-by-Step Solution:
1. Understand Standard Form: Standard form, or scientific notation, is a way to express numbers that are too big or too small in a more concise format. It generally follows the structure:
[tex]\[ a \times 10^n \][/tex]
where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
2. Identify the Number: Here, the number in question is 165,000.
3. Transform to Standard Form:
- Write 165,000 as a product of a number between 1 and 10, and a power of 10.
- To do this, move the decimal point in 165,000 to the left until only one non-zero digit remains on the left:
[tex]\[ 165,000 = 1.65 \times 10^5 \][/tex]
4. Verify the Options:
- A. [tex]\( 1.65 \times 10^3 \)[/tex]
- This would represent 1,650, which is not correct.
- B. [tex]\( 1.65 \times 10^5 \)[/tex]
- This represents [tex]\( 1.65 \times 10^{5} = 165,000 \)[/tex], which is correct.
- C. [tex]\( 1.65 \times 10^{-5} \)[/tex]
- This represents a very small number, [tex]\( 0.0000165 \)[/tex], which is incorrect.
- D. [tex]\( 1.65 \times 10^{-3} \)[/tex]
- This represents [tex]\( 0.00165 \)[/tex], which is also incorrect.
Therefore, the correct choice is:
B. [tex]\( 1.65 \times 10^5 \)[/tex]
