To express numbers in exponential notation, we convert them into a form where they are represented as a product of a number between 1 and 10, and a power of 10. Let's look at the step-by-step solutions:
### Part (a) 12,500
1. Identify the significant part of the number, which is 1.25 in this case, since we need to place the decimal point after the first non-zero digit.
2. Determine how many places the decimal point needs to be moved to recreate the original number:
- We have 12,500.
- Moving the decimal point four places to the left gives us 1.2500.
3. This movement of the decimal point is represented as [tex]\(10^4\)[/tex].
Hence, 12,500 can be written in exponential notation as:
[tex]\[ 1.25 \times 10^4 \][/tex]
### Part (b) -343
1. Identify the significant part of the number, which is -3.43 in this case, since we place the decimal point after the first non-zero digit.
2. Determine how many places the decimal point needs to be moved to recreate the original number:
- We have -343.
- Moving the decimal point two places to the left gives us -3.43.
3. This movement of the decimal point is represented as [tex]\(10^2\)[/tex].
Hence, -343 can be written in exponential notation as:
[tex]\[ -3.43 \times 10^2 \][/tex]
So, the numbers expressed in exponential notation are:
- (a) [tex]\(1.25 \times 10^4\)[/tex]
- (b) [tex]\(-3.43 \times 10^2\)[/tex]
