Convert 3/16
to a decimal using long division.
To convert 3/16 to a decimal using long division, follow these steps:
Step 1: Set up the division problem
Write down 0. followed by a vertical bar (|) to represent the decimal point, and place the dividend (3) inside the long division bracket. Then place the divisor (16) outside the division bracket.
0.| 3
-----
16
Step 2: Divide the first digit
Since 3 is less than 16, we need to add a decimal place to the right and bring down the next digit of the dividend. Write down 0.1 on top of the division line and multiply 0.1 by 16.
0.| 3
-----
16
- 0 (0.1 x 16)
Step 3: Subtract the result of the multiplication from the dividend
Subtract the result of the multiplication (0) from the previous step from the dividend (3).
0.| 3
-----
16
- 0 (0.1 x 16)
-----
3
Step 4: Bring down the next digit
Bring down the next digit from the dividend, which is 0. Write it next to the previous remainder.
0.| 3
-----
16
- 0 (0.1 x 16)
-----
30
Step 5: Divide and multiply
Since 30 is greater than 16, we can divide 30 by 16 to get the next decimal digit. Write down the quotient (1) on top of the division line and multiply 1 by 16.
0.| 3
-----
16
- 0 (0.1 x 16)
-----
30
-16 (1 x 16)
Step 5: Subtract the result of the multiplication from the previous remainder
Subtract the result of the multiplication (16) from the previous step from the remainder (30).
0.| 3
-----
16
- 0 (0.1 x 16)
-----
30
-16 (1 x 16)
------
14
Step 6: Bring down the next digit and repeat
Bring down the next digit from the dividend, which is 0.
0.| 3
-----
16
- 0 (0.1 x 16)
-----
30
-16 (1 x 16)
------
14
0
Since the dividend (14) is less than the divisor (16), we know the division will have a remainder and terminate the long division process.
The decimal representation of 3/16 is 0.1875.
To convert 3/16 to a decimal using long division, follow these steps:
1. Write 3 as the dividend and 16 as the divisor.
_____
16 | 3
2. Divide the first digit of the dividend (3) by the divisor (16) to get the quotient.
3 ÷ 16 = 0.1875 (write 0.1 above the division symbol)
0.1
_____
16 | 3
3. Multiply the divisor (16) by the quotient (0.1) and subtract the result from the dividend (3).
3 - (16 × 0.1) = 3 - 1.6 = 1.4 (write 1.4 under the line)
0.1
_____
16 | 3
- 1.6
4. Bring down the next digit from the dividend, which is 0.
0.1
_____
16 | 3
- 1.6
0
5. Divide the new dividend (14) by the divisor (16) to get the next digit of the quotient.
14 ÷ 16 = 0.0875 (write 0.0875 above the line)
0.1 0.0875
_____
16 | 3
- 1.6
0
6. Multiply the divisor (16) by the new quotient digit (0.0875) and subtract the result from the dividend (14).
14 - (16 × 0.0875) = 14 - 1.4 = 12.6 (write 12.6 under the line)
0.1 0.0875
_____
16 | 3
- 1.6
0
-12.6
7. Continue to bring down more zeros and perform the long division until you have reached the desired level of precision.
- Since the remainder (12.6) is less than the divisor (16), we can conclude that the division is finished.
Therefore, 3/16 in decimal form is approximately 0.1875.
To convert 3/16 to a decimal using long division, follow these steps:
Step 1: Write down the division problem.
Divide 3 by 16.
Step 2: Set up the long division.
Start by placing the divisor, 16, on the outside of the division bracket and the dividend, 3, inside the bracket. Place a decimal point above the division bracket in the quotient.
0.
-------
16 | 3
Step 3: Determine the first digit of the quotient.
Ask yourself, how many times does 16 go into 3? Since 16 is larger than 3, the first digit of the quotient will be 0.
0.
-------
16 | 3
Step 4: Bring down the next digit.
Write a 0 after the 3, next to the decimal point. This is called bringing down the next digit.
0.
-------
16 | 30
Step 5: Divide the new dividend by the divisor.
Ask yourself, how many times does 16 go into 30? The largest multiple of 16 that is less than or equal to 30 is 16, which goes into 30 one time. Write 1 above the division bracket, and place a 16 underneath the dividend.
0.1
-------
16 | 30
16
Step 6: Subtract.
Subtract the product of the divisor (16) and the quotient digit (1) from the dividend. Write the result below the line.
0.1
-------
16 | 30
-16
----
14
Step 7: Bring down the next digit.
Write a 0 after the 14, next to the decimal point.
0.1
-------
16 | 30
-16
----
14
0
Step 8: Divide the new dividend by the divisor.
Ask yourself, how many times does 16 go into 140? The largest multiple of 16 that is less than or equal to 140 is 8, which goes into 140 eight times. Write 8 above the division bracket, and place a 16 underneath the new dividend.
0.18
-------
16 | 30
-16
----
14
08
----
20
Step 9: Subtract.
Subtract the product of the divisor (16) and the quotient digit (8) from the dividend. Write the result below the line.
0.18
-------
16 | 30
-16
----
14
08
----
20
-16
----
4
Step 10: Bring down the next digit.
Write a 0 after the 4, next to the decimal point.
0.1875
-------
16 | 30
-16
----
14
08
----
20
-16
----
4
0
Step 11: Divide the new dividend by the divisor.
Ask yourself, how many times does 16 go into 40? The largest multiple of 16 that is less than or equal to 40 is 2, which goes into 40 twice. Write 2 above the division bracket, and place a 16 underneath the new dividend.
0.1875
-------
16 | 30
-16
----
14
08
----
20
-16
----
4
0
32
Step 12: Subtract.
Subtract the product of the divisor (16) and the quotient digit (2) from the dividend. Write the result below the line.
0.1875
-------
16 | 30
-16
----
14
08
----
20
-16
----
4
0
32
-32
----
0
Step 13: The remainder is 0.
Since there is no remainder, the long division is complete. The quotient, when written as a decimal, is 0.1875. Therefore, 3/16 can be represented as the decimal 0.1875.