Use long division to convert 2 5/6 to a decimal. Round to the nearest hundredth.
*
1 point
2.83
To convert 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: Perform the long division by dividing the numerator (17) by the denominator (6).
2.83...
-------------
6 ) 17.00
- 12
--
58
- 54
--
40
- 36
--
40
- 36
--
4
Step 3: Continue the division until you have the desired number of decimal places or until the remainder becomes zero. In this case, the remainder is 4, and since the pattern of 36 repeats, the decimal form is 2.83.
Therefore, 2 5/6 as a decimal, rounded to the nearest hundredth, is 2.83.
To convert the mixed number 2 5/6 to a decimal, you can use long division.
Step 1: Divide the whole number part, which is 2, by the denominator (6).
2 ÷ 6 = 0.3
Step 2: Divide the numerator (5) by the denominator (6).
5 ÷ 6 ≈ 0.8333 (rounded to four decimal places)
Step 3: Add the quotient from Step 1 and the decimal from Step 2.
0.3 + 0.8333 = 1.1333 (rounded to four decimal places)
Therefore, converting the mixed number 2 5/6 to a decimal, rounded to the nearest hundredth, is approximately 1.13.
To convert a mixed number like 2 5/6 to a decimal using long division, follow these steps:
Step 1: Write the mixed number as a fraction. In this case, 2 5/6 can be written as (2 * 6 + 5)/6 = 17/6.
Step 2: Perform long division by dividing the numerator (17) by the denominator (6). Write the dividend (17) inside the division symbol and the divisor (6) outside the division symbol.
2.83
---------------
6 | 17
Step 3: Start dividing. Divide 6 into 17, and write the quotient above the dividend.
2.83
---------------
6 | 17
- 12
-----
5
Step 4: Multiply the remainder (5) by 10 to bring down the next digit. Write the result under the remainder.
2.83
---------------
6 | 17
- 12
-----
5
50
Step 5: Divide the new number by the divisor (6) and write the quotient on top with a decimal point.
2.833
---------------
6 | 17
- 12
-----
5
50
--
20
Step 6: Repeat steps 4 and 5 until you have the desired level of precision (in this case, round to the nearest hundredth).
2.8333...
---------------
6 | 17
- 12
-----
5
50
--
20
18
----
20
18
----
20
18
----
20
Since we have reached the desired level of precision, we can round the decimal to the nearest hundredth. In this case, 2.833 is rounded to 2.83.
So, 2 5/6 is approximately equal to 2.83 (rounded to the nearest hundredth).