Use long division to convert 3 3/8 to a decimal.(1 point)
Responses
0.375
0.375
33.75
33.75
3.375
3.375
2.66
0.375
To convert a mixed number like 3 3/8 to a decimal, you can use long division. Here are the steps:
1. Start by dividing the whole number (3) by the denominator (8). 3 divided by 8 equals 0 with a remainder of 3.
0. | 3 3/8
---------------------
8 | 3
2. Bring down the next digit, which is 3, and place it after the remainder. Now you have 33.
0. | 3 3/8
---------------------
8 | 33
3. Divide 33 by the denominator (8). 33 divided by 8 equals 4 with a remainder of 1.
0.4 | 3 3/8
---------------------
8 | 33
- 32
----
1
4. Bring down the next digit, which is 0, and place it after the remainder. Now you have 10.
0.43 | 3 3/8
---------------------
8 | 33
- 32
----
10
5. Divide 10 by the denominator (8). 10 divided by 8 equals 1 with a remainder of 2.
0.437 | 3 3/8
---------------------
8 | 33
- 32
----
10
- 8
--
2
6. Bring down the next digit, which is 0, and place it after the remainder. Now you have 20.
0.4375 | 3 3/8
---------------------
8 | 33
- 32
----
10
- 8
--
20
7. Divide 20 by the denominator (8). 20 divided by 8 equals 2 with a remainder of 4.
0.4375 | 3 3/8
---------------------
8 | 33
- 32
----
10
- 8
--
2
- 0
--
20
8. Finally, bring down the last digit, which is 0, and divide by the denominator (8). 0 divided by 8 equals 0.
0.4375 | 3 3/8
---------------------
8 | 33
- 32
----
10
- 8
--
2
- 0
--
20
- 16
-----
40
Based on these calculations, the decimal equivalent of 3 3/8 is 3.375.
To convert a mixed number like 3 3/8 to a decimal, you can use long division. Here's how:
1. Write the mixed number as a fraction. In this case, 3 3/8 can be written as a fraction: 35/8.
- The whole number part (3) becomes the numerator.
- The fraction part (3/8) retains its numerator and denominator.
2. Perform long division with 35 as the dividend and 8 as the divisor. Divide 35 by 8:
- Start by dividing the first digit, 3, by 8. The quotient is 0 with a remainder of 3.
- Bring down the next digit, which is 5, to the right of the remainder. Now you have 35.
- Divide the new number, 35, by 8. The quotient is 4 with a remainder of 3.
- Since the remainder is not zero, you can continue the division process by bringing down more digits after the remainder.
3. Continue dividing until you have the desired level of accuracy or until you observe a pattern:
- Bring down another digit, 0, to the right of the remainder. Now you have 30.
- Divide 30 by 8. The quotient is 3 with a remainder of 6.
- Bring down another digit, 0, to the right of the remainder. Now you have 60.
- Divide 60 by 8. The quotient is 7 with a remainder of 4.
- Bring down another digit, 0, to the right of the remainder. Now you have 40.
- Divide 40 by 8. The quotient is 5 with no remainder.
4. Check for a repeating pattern:
- If there is no remainder throughout the division process and the process terminates, the decimal representation is exact.
- If there is a remainder and the division process repeats a pattern, the decimal representation will be a repeating decimal.
In this case, the division process does not repeat, and the decimal representation is exact. The final quotient will be 3.375.
Therefore, the correct answer is 3.375.