Use long division to convert 2 71/6 to a decimal...
To convert a mixed number to a decimal using long division, follow these steps:
Step 1: Set up the division problem
Write the whole number part of the mixed number (2) as the dividend, and the fraction part (71/6) as the divisor.
2 71/6
Step 2: Convert the fraction to a decimal
To convert the fraction 71/6 to a decimal, divide the numerator (71) by the denominator (6).
11.83333...
Step 3: Perform long division
Now, you will perform long division. Place a decimal point above the line and add a zero after the decimal point in the dividend.
2. | 71/6
- 60
-----
110
- 108
-----
20
...
Continue the long division process until you reach the desired level of decimal places or until the pattern repeats.
Step 4: Write the final decimal answer
The final decimal is 11.83333... (which can also be written as 11.83 or rounded to the desired degree of accuracy).
Therefore, 2 71/6 as a decimal is approximately 11.83.
To convert the mixed number 2 71/6 to a decimal using long division, follow these steps:
Step 1: Set up the long division problem by writing 71/6 as a fraction.
2 71/6 = 2 + 71/6
Step 2: Convert the mixed number to an improper fraction.
2 71/6 = (2 * 6 + 71)/6
= (12 + 71)/6
= 83/6
Step 3: Perform long division by dividing the numerator by the denominator.
83 ÷ 6
13.8333...
-----------
6 │83
Step 4: Start by dividing 83 by 6. The quotient is 13 and the remainder is 5. Write the remainder as a fraction with the denominator of 6.
83 ÷ 6 = 13 remainder 5
83/6 = 13 + 5/6
Step 5: Bring down the next digit, which is zero.
83/6 = 13 5/6
Step 6: Place a decimal point at the top of the division bar. Add a zero to the right of the remainder and continue dividing by 6.
83/6 = 13.5
13.83333...
-----------
6 │83.0
Step 7: Divide 50 by 6. The quotient is 8 and the remainder is 2. Write the remainder as a fraction with the denominator of 6.
50 ÷ 6 = 8 remainder 2
50/6 = 8 + 2/6
Step 8: Bring down the next digit, which is zero.
50/6 = 8 2/6
50/6 = 8.2
13.8333333...
----------------
6 │83.05
Step 9: Divide 20 by 6. The quotient is 3 and the remainder is 2. Write the remainder as a fraction with the denominator of 6.
20 ÷ 6 = 3 remainder 2
20/6 = 3 + 2/6
Step 10: Bring down the next digit, which is zero.
20/6 = 3 2/6
20/6 = 3.33...
13.8333333333...
------------------
6 │83.055
Step 11: Divide 20 by 6 again. The quotient is 3 and the remainder is 2. Write the remainder as a fraction with the denominator of 6.
20 ÷ 6 = 3 remainder 2
20/6 = 3 + 2/6
Step 12: Bring down the next digit, which is zero.
20/6 = 3 2/6
20/6 = 3.333...
13.833333333333...
-------------------
6 │83.0555
Step 13: Continue the process indefinitely to calculate more decimal places if needed. However, note that the division will not terminate since the fraction 71/6 is a repeating decimal.
To convert the mixed number 2 71/6 to a decimal using long division, follow these steps:
Step 1: Convert the mixed number to an improper fraction.
To do this, multiply the whole number (2) by the denominator (6), and then add the numerator (71).
2 * 6 + 71 = 83.
So, the improper fraction equivalent is 83/6.
Step 2: Perform the long division.
Divide the numerator (83) by the denominator (6). Here's how:
13
______
6 | 83
Start by dividing 8 by 6, which is 1. Write the quotient (1) above the line, next to the 13.
13
1 ____
6 | 83
Multiply the quotient (1) by the divisor (6) to get 6, and subtract it from the numerator (83 - 6 = 77). Write the result below the line.
13
1 ____
6 | 83
- 6
-----
77
Now, bring down the next digit, which is 7.
13
1 ____
6 | 83
- 6
-----
77
6
Divide 77 by 6, which gives 12. Write the quotient (12) above the line, next to the 1.
13
12____
6 | 83
- 6
-----
77
6
Multiply 12 by 6 to get 72, and subtract it from 77 (77 - 72 = 5). Write the result (5) below the line.
13
12_____
6 | 83
- 6
-----
77
6
5
Step 3: Continue the long division.
Since there are no more digits to bring down, we can stop the division. The remainder is 5, and there is no pattern of repeating decimals.
Step 4: Write the final decimal answer.
To convert the fraction 5/6 to a decimal, divide the numerator (5) by the denominator (6).
5 ÷ 6 = 0.83333...
Therefore, 2 71/6 as a decimal is approximately 2.83333... or 2.83 (rounded to two decimal places).