Express the number 45000 in exponential notation to show two significant figures

The correct option is 4.5x(10)⁴.

Let us break down the logical steps to express the number 45000 in exponential notation with exactly two significant figures:

Step 1: Understand Exponential (Scientific) Notation
Exponential notation is written in the general form:

$$a\times {10}^n$$

Step 2: Convert the Number 45000
To convert 45000 to this form, we place the decimal point after the first non-zero digit (4), which gives us 4.5. To keep the value equal to 45000, we count how many places we moved the decimal point to the left:
45000.0 → 4.50000 (moved 4 places to the left).
Therefore, the number is written as:

$$4.5\times {10}^4$$

Step 3: Verify the Number of Significant Figures
The question specifies that the final value must show exactly two significant figures.
In exponential notation, all digits in the coefficient ($a$) are significant.
Looking at the coefficient 4.5:
- The digit 4 is significant.
- The digit 5 is significant.
This gives us exactly two significant figures.
If we wrote it as 4.50x(10)⁴, it would have three significant figures. If we wrote it as 4.500x(10)⁴, it would have four significant figures. Thus, 4.5x(10)⁴ is the correct representation.