Let's analyze the problem step by step:
We start with the number [tex]\(5,000,000,000,000,000\)[/tex].
### Statement A:
To divide the number by [tex]\(10^5\)[/tex], remove 5 zeros from the end of the number.
- Dividing [tex]\(5,000,000,000,000,000\)[/tex] by [tex]\(10^5\)[/tex]:
[tex]\[
\frac{5,000,000,000,000,000}{100,000} = 50,000,000,000
\][/tex]
- Removing 5 zeros from the end of the number [tex]\(5,000,000,000,000,000\)[/tex]:
[tex]\[
5,000,000,000,000,000 \rightarrow 50,000,000,000
\][/tex]
Both operations yield [tex]\(50,000,000,000\)[/tex], so statement A is correct.
### Statement B:
To divide the number by [tex]\(10^8\)[/tex], remove 7 zeros from the end of the number.
- Dividing [tex]\(5,000,000,000,000,000\)[/tex] by [tex]\(10^8\)[/tex]:
[tex]\[
\frac{5,000,000,000,000,000}{100,000,000} = 50,000,000
\][/tex]
- Removing 7 zeros from the end of the number [tex]\(5,000,000,000,000,000\)[/tex]:
[tex]\[
5,000,000,000,000,000 \rightarrow 50,000,000,000
\][/tex]
Removing 7 zeros results in [tex]\(50,000,000,000\)[/tex], but the division yields [tex]\(50,000,000\)[/tex]. Therefore, statement B is incorrect.
### Statement C:
To divide the number by [tex]\(10^{10}\)[/tex], remove 10 zeros from the end of the number.
- Dividing [tex]\(5,000,000,000,000,000\)[/tex] by [tex]\(10^{10}\)[/tex]:
[tex]\[
\frac{5,000,000,000,000,000}{10,000,000,000} = 500,000
\][/tex]
- Removing 10 zeros from the end of the number [tex]\(5,000,000,000,000,000\)[/tex]:
[tex]\[
5,000,000,000,000,000 \rightarrow 500,000
\][/tex]
Both operations yield [tex]\(500,000\)[/tex], so statement C is correct.
### Statement D:
To divide the number by [tex]\(10^{13}\)[/tex], remove 14 zeros from the end of the number.
- Dividing [tex]\(5,000,000,000,000,000\)[/tex] by [tex]\(10^{13}\)[/tex]:
[tex]\[
\frac{5,000,000,000,000,000}{10,000,000,000,000} = 500
\][/tex]
- Removing 14 zeros from the end of the number [tex]\(5,000,000,000,000,000\)[/tex]:
[tex]\[
5,000,000,000,000,000 \rightarrow 50
\][/tex]
Removing 14 zeros results in [tex]\(50\)[/tex], but the division yields [tex]\(500\)[/tex]. Therefore, statement D is incorrect.
### Conclusion:
The correct statements are:
- A. To divide the number by [tex]\(10^5\)[/tex], remove 5 zeros from the end of the number.
- C. To divide the number by [tex]\(10^{10}\)[/tex], remove 10 zeros from the end of the number.
