Use long division to convert 2 5/6 to a decimal. Round to the nearest hundredth.
To convert 2 5/6 to a decimal using long division:
1. Write 2 as the whole number part and 5/6 as the fractional part.
2. Multiply the denominator of the fractional part (6) by a number that gives a product less than or equal to the numerator (5). In this case, 6 * 1 = 6.
3. Write 1 as the whole number part and 0 as the fractional part in the quotient.
4. Subtract the product (6) from the numerator (5). 5 - 6 = -1. Bring down the next digit (0).
5. Write -1 as the numerator and 6 as the denominator.
6. Multiply the denominator of the fractional part (6) by a number that gives a product less than or equal to the numerator (-1). In this case, 6 * -1 = -6.
7. Write -1 as the whole number part and -1 as the fractional part in the quotient.
8. Subtract the product (-6) from the numerator (-1). -1 - (-6) = 5. Bring down the next digit (0).
9. Write 5 as the numerator and 6 as the denominator.
10. Multiply the denominator of the fractional part (6) by a number that gives a product less than or equal to the numerator (5). In this case, 6 * 0 = 0.
11. Write 0 as the whole number part and 0 as the fractional part in the quotient.
12. Subtract the product (0) from the numerator (5). 5 - 0 = 5.
13. Write 5 as the numerator and 6 as the denominator.
14. Multiply the denominator of the fractional part (6) by a number that gives a product less than or equal to the numerator (5). In this case, 6 * 0 = 0.
15. Write 0 as the whole number part and 0 as the fractional part in the quotient.
16. Subtract the product (0) from the numerator (5). 5 - 0 = 5.
17. Since no more digits remain, the division is complete.
18. The decimal representation of 2 5/6 is approximately 2.83 when rounded to the nearest hundredth.
To convert the mixed number 2 5/6 into a decimal using long division, follow these steps:
Step 1: Convert the mixed number to an improper fraction.
Multiply the whole number by the denominator and add the numerator. In this case, since the whole number is 2 and the fraction is 5/6:
2 * 6 + 5 = 12 + 5 = 17
So, the improper fraction is 17/6.
Step 2: Divide the numerator (17) by the denominator (6) using long division.
Divide 17 by 6:
____
6 | 17
-12
__
5
Step 3: Write the decimal.
The quotient is 2 with a remainder of 5. Since the decimal is rounded to the nearest hundredth, the remainder is divided by the denominator and added to the quotient:
5/6 = 0.83 (rounded to two decimal places)
Step 4: Add the integer part.
Since the whole number was 2, add it to the decimal:
2 + 0.83 = 2.83
Therefore, 2 5/6 is approximately equal to 2.83 when rounded to the nearest hundredth.
To convert the mixed number 2 5/6 to a decimal using long division, follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
2 5/6 = (2 * 6 + 5)/6
= 17/6
Step 2: Set up the long division. Write 17/6 as a numerator outside the division bar and 6 as a denominator inside the division bar. Place the decimal point above the division bar directly above the division symbol.
____
6 | 17.00
Step 3: Divide the first digit of the numerator (1) by the denominator (6). The result is 0 with a remainder of 1. Write the quotient (0) above the division bar.
0.
6 | 17.00
0
Step 4: Bring down the next digit from the numerator (7) next to the remainder (1). This gives us 17.
0.
6 | 17.00
0
17
Step 5: Divide the new numerator (17) by the denominator (6). The result is 2 with a remainder of 5. Write the quotient (2) next to the previous quotient (0).
0.2
6 | 17.00
0
17
12
Step 6: Bring down the next digit from the numerator (0) next to the remainder (5). This gives us 50.
0.28
6 | 17.00
0
17
12
50
Step 7: Divide the new numerator (50) by the denominator (6). The result is 8 with a remainder of 2. Write the quotient (8) next to the previous quotients (0 and 2).
0.28 3
6 | 17.00
0
17
12
50
48
Step 8: Bring down the next digit from the numerator (0) next to the remainder (2). This gives us 20.
0.2833
6 | 17.00
0
17
12
50
48
20
Step 9: Divide the new numerator (20) by the denominator (6). The result is 3 with a remainder of 2. Write the quotient (3) next to the previous quotients (0, 2, and 8).
0.28333
6 | 17.00
0
17
12
50
48
20
18
Step 10: Bring down another digit from the numerator (0) next to the remainder (2). This gives us 20 again.
0.283333
6 | 17.00
0
17
12
50
48
20
18
20
Step 11: Divide the new numerator (20) by the denominator (6). The result is 3 with a remainder of 2. Write the quotient (3) next to the previous quotients (0, 2, 8, and 3).
0.283333...
6 | 17.00
0
17
12
50
48
20
18
20
18
Step 12: Continue this process of long division until you reach the desired level of precision or until the decimal terminates or repeats.
Step 13: Round the decimal to the nearest hundredth. In this case, the hundredth place is three decimal places after the decimal point. Therefore, the rounded decimal is 0.28.
Therefore, 2 5/6 is approximately equal to 0.28 when rounded to the nearest hundredth.