Use long division to convert 5 3/16 to a decimal
0.1875
5.1875
~5.3
5.36
To convert 5 3/16 to a decimal using long division, follow these steps:
1. Rewrite the mixed number as an improper fraction. Multiply the whole number (5) by the denominator of the fraction (16) and add the numerator (3) to get the new numerator. The denominator remains the same.
5 × 16 + 3 = 80 + 3 = 83
The improper fraction is 83/16.
2. Perform long division by dividing the numerator (83) by the denominator (16).
5. remainder: 3
----
16 | 83
80
---
3
3. Add a decimal point to the quotient (5) and bring down a zero.
5.0
----
16 | 83
80
---
30
4. Divide the new dividend (30) by the divisor (16).
5.18 remainder: 14
------
16 | 83.0
80
----
30
16
---
14
5. Bring down another zero and continue dividing.
5.187 remainder: 144
------
16 | 83.00
80
----
30
16
---
144
6. The remainder (144) is greater than the divisor (16), so bring down another zero.
5.1875 remainder: 1440
------
16 | 83.000
80
-----
30
16
----
144
128
----
160
-----
1440
7. The remainder is now 1440. Since it is greater than the divisor (16), continue bringing down zeros and dividing until the desired level of precision is reached.
5.1875 remainder: 1440
------
16 | 83.0000
80
-----
30
16
----
144
128
----
160
-----
1440
1440
-----
0
8. The remainder becomes 0, indicating that the division process is complete. The quotient is 5.1875.
Therefore, 5 3/16 as a decimal is 5.1875.
To convert 5 3/16 to a decimal using long division, follow these steps:
1. Rewrite the mixed number as an improper fraction: 5 3/16 = (5 * 16 + 3) / 16 = 83/16.
2. Set up the long division problem by dividing 83 by 16.
3. Start dividing. Since 16 is smaller than 83, the largest multiple of 16 that fits into 83 is 5 (16 * 5 = 80).
4. Subtract 80 from 83. This leaves you with a remainder of 3.
5. Bring down the next digit from the decimal, which is 0. Add it to the remainder to get 30.
6. Divide 30 by 16, finding that the largest multiple of 16 that fits into 30 is 1 (16 * 1 = 16).
7. Subtract 16 from 30. This leaves you with a remainder of 14.
8. Bring down the next digit from the decimal, which is 0. Add it to the remainder to get 140.
9. Divide 140 by 16, finding that the largest multiple of 16 that fits into 140 is 8 (16 * 8 = 128).
10. Subtract 128 from 140. This leaves you with a remainder of 12.
11. Bring down the next digit from the decimal, which is 5. Add it to the remainder to get 125.
12. Divide 125 by 16, finding that the largest multiple of 16 that fits into 125 is 7 (16 * 7 = 112).
13. Subtract 112 from 125. This leaves you with a remainder of 13.
14. Bring down the next digit from the decimal, which is 0.
15. Divide 130 by 16, finding that the largest multiple of 16 that fits into 130 is 8 (16 * 8 = 128).
16. Subtract 128 from 130. This leaves you with a remainder of 2.
17. Bring down the next digit from the decimal, which is 0.
18. Divide 20 by 16, finding that the largest multiple of 16 that fits into 20 is 1 (16 * 1 = 16).
19. Subtract 16 from 20. This leaves you with a remainder of 4.
20. Since the remainder is 4, you can stop the division process.
21. The final result is 5.3125.
Therefore, the correct answer is 5.3125.
To convert a mixed number like 5 3/16 to a decimal, you can use long division. Here's how to do it:
Step 1: Set up the division problem by putting the mixed number (5 3/16) as the dividend and 16 as the divisor.
5 3/16 ÷ 16
Step 2: Convert the mixed number to an improper fraction. Multiply the whole number (5) by the denominator of the fraction (16) and add the numerator (3). Write this sum over the original denominator.
5 × 16 + 3
--------------
16
= 83/16
Step 3: Begin the long division process. Divide the numerator (83) by the denominator (16) and write the quotient above the line.
5 3/16 ÷ 16
_______
| 5
Step 4: Multiply the divisor (16) by the quotient (5) and subtract the result from the numerator (83).
5 3/16 ÷ 16
_______
16| 83
-80
----
3
Step 5: Since we have a remainder of 3, bring down the next digit from the original mixed number. In this case, it's 0.
5 3/16 ÷ 16
_______
16| 83
-80
----
30
Step 6: Repeat the division process. Divide the new numerator (30) by the denominator (16) and write the quotient above the line.
5 3/16 ÷ 16
_______
16| 83
-80
----
30
16
----
14
Step 7: Again, we have a remainder of 14, so bring down the next digit from the original mixed number. In this case, it's 0.
5 3/16 ÷ 16
_______
16| 83
-80
----
30
16
----
140
Step 8: Continue the division. Divide the new numerator (140) by the denominator (16) and write the quotient above the line.
5 3/16 ÷ 16
_______
16| 83
-80
----
30
16
----
140
-128
----
128
Step 9: Bring down the last digit from the original mixed number, which is 0.
5 3/16 ÷ 16
_______
16| 83
-80
----
30
16
----
140
-128
----
128
128
----
0
Step 10: The division is complete when there is a remainder of 0. The quotient above the line represents the integer part of the decimal, and the fractional part is the remainder.
5 3/16 ÷ 16 = 5.1875
Therefore, the decimal equivalent of 5 3/16 is 5.1875.