The earth is 4,540,000,000
years old.
If this number is written in scientific notation, what is the value of the exponent on 10
?
Responses
4
4
5
5
7
7
9
9
The value of the exponent on 10 in scientific notation for the age of the Earth, which is 4,540,000,000 years old, is 9.
To determine the value of the exponent on 10 when writing the age of the Earth in scientific notation, we need to convert the number 4,540,000,000 to a number between 1 and 10, while keeping track of how many places we move the decimal point.
Here's the step-by-step process to find the value of the exponent:
1. Start with the number 4,540,000,000.
2. Count the number of zeros after the 4 (there are eight zeros).
3. Move the decimal point in the number 4,540,000,000 to the left eight places. This will make the number between 1 and 10.
- The decimal point would be moved to the left by one place to get 454,000,000.
- Moving it another place gives 45,400,000.
- Another place gives 4,540,000.
- Moving it four more places to the left yields 45,400.
- Another place gives 4,540.
- Moving it two more places gives 45.4.
- Finally, moving it one more place to the left results in 4.54.
4. Since we had to move the decimal point to the left eight places to obtain 4.54, the exponent on 10 is 8.
Therefore, the correct answer is: 7