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

Question

Responses

5.1875
5.1875

≈5.3
approximately equals 5.3

5.36
5.36

0.1875
0.1875

Answer 1

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.