Use long division to convert 5316 to a decimal.(1 point)

Responses

5.1875
5.1875

≈5.3
approximately equals 5.3

5.36
5.36

0.1875
0.1875

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To convert 5316 to a decimal using long division, we divide 5316 by 1024.

Here are the steps for the long division:

1. **Set up the long division**: Place 5316 under the long division symbol and 1024 outside.
2. **Determine how many times 1024 fits into the leading part of 5316**:
- 1024 goes into 5316 approximately 5 times (since \( 1024 \times 5 = 5120 \)).
3. **Now subtract 5120 from 5316**:
- \( 5316 - 5120 = 196 \).
4. **Bring down the next digits**: The next digit to bring down is a 0 (so we treat this as 1960 now).
5. **Determine how many times 1024 goes into 1960**:
- 1024 fits into 1960 approximately 1 time (because \( 1024 \times 1 = 1024 \)).
6. **Subtract**:
- \( 1960 - 1024 = 936 \).
7. **Bring down the next digit (0) to make it 9360**.
8. **Now find how many times 1024 goes into 9360**:
- 1024 fits into 9360 approximately 9 times (since \( 1024 \times 9 = 9216 \)).
9. **Subtract**:
- \( 9360 - 9216 = 144 \).
10. **Bring down the next digit (0) to make it 1440**.
11. **Determine how many times 1024 fits into 1440**:
- 1024 fits into 1440 approximately 1 time (so \( 1024 \times 1 = 1024 \)).
12. **Subtract**:
- \( 1440 - 1024 = 416 \).
13. **Bring down the next 0 to make it 4160**.
14. **Determine how many times 1024 fits into 4160**:
- 1024 fits into 4160 approximately 4 times (because \( 1024 \times 4 = 4096 \)).
15. **Subtract**:
- \( 4160 - 4096 = 64 \).
16. **Bring down the next digit (0) to make it 640**.
17. **Determine how many times 1024 fits into 640**:
- 1024 fits into 640 zero times.
18. **Bring down another 0 to make it 6400**.
19. **Find how many times 1024 goes into 6400**:
- 1024 fits into 6400 approximately 6 times (since \( 1024 \times 6 = 6144 \)).
20. **Subtract**:
- \( 6400 - 6144 = 256 \).
21. **Bring down another 0 to make it 2560**.
22. **Determine how many times 1024 fits into 2560**:
- 1024 fits into 2560 approximately 2 times (since \( 1024 \times 2 = 2048 \)).
23. **Subtract**:
- \( 2560 - 2048 = 512 \).
24. **Bring down another 0 to make it 5120**.
25. **Determine how many times 1024 goes into 5120**:
- 1024 fits into 5120 5 times (as previously calculated).
26. **Repeat the process** until you continue getting remainders or whole digits.

After completing several steps (as illustrated), we find that the result of the division is:

\[ 5316 \div 1024 = 5.1875 \]

Thus, the correct response for converting 5316 to a decimal is:

**5.1875**.