Question

Use long division to convert 3/16 to a decimal.(1 point)

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Answer 1

[AI-generated answer — Bot GPT 3.5]

To convert the fraction 3/16 to a decimal using long division, follow these steps:

1. Set up the division problem with 3 as the numerator and 16 as the denominator, placing the decimal point in the quotient above the division bar.

0.
____
16 | 3.00

2. Divide 3 by 16, which gives 0 as the quotient.

0.
____
16 | 3.00
0

3. Multiply the quotient (0) by 16 and subtract from 3. Write the result (3) under the line.

0.
______
16 | 3.00
- 0
_______
3

4. Bring down the next digit (0) after the decimal point.

0.
______
16 | 3.00
- 0
_______
30

5. Divide 30 by 16, which gives 1. Write 1 as the next digit in the quotient.

0.1
______
16 | 3.00
- 0
_______
30
16
______
14

6. Multiply the quotient (0.1) by 16 and subtract from 30. Write the result (14) under the line.

0.1
______
16 | 3.00
- 0
_______
30
16
______
14

7. Keep bringing down the next digit (0) after the decimal point and continue the process until you get the desired level of accuracy.

In this case, the process will continue indefinitely since 3/16 is a repeating decimal. The decimal representation of 3/16 is 0.1875.

Answer 2

Use long division to convert 11/20 to a decimal.(1 point)

Answer 3

[AI-generated answer — Bot GPT 3.5]

To convert the fraction 11/20 to a decimal using long division, follow these steps:

1. Set up the division problem with 11 as the numerator and 20 as the denominator, placing the decimal point in the quotient above the division bar.

0.
____
20 | 11.00

2. Divide 11 by 20, which gives 0 as the quotient.

0.
____
20 | 11.00
0

3. Multiply the quotient (0) by 20 and subtract from 11. Write the result (11) under the line.

0.
______
20 | 11.00
- 0
_______
11

4. Bring down the next digit (0) after the decimal point.

0.
______
20 | 11.00
- 0
_______
11
0

5. Divide 110 by 20, which gives 5 as the quotient.

0.5
______
20 | 11.00
- 0
_______
11
0
______
110

6. Multiply the quotient (0.5) by 20 and subtract from 110. Write the result (10) under the line.

0.5
______
20 | 11.00
- 0
_______
11
0
______
110

7. Since no more digits remain, the long division is complete.

In this case, the decimal representation of 11/20 is 0.55.

Answer 4

Use long division to convert 3 4/5 to a decimal.(1 point)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To convert the mixed number 3 4/5 to a decimal using long division, follow these steps:

1. Convert the mixed number into an improper fraction. Multiply the whole number (3) by the denominator (5) and add the numerator (4). Write the sum (19) over the denominator.

3 4/5 = ((3 * 5) + 4) / 5 = 19/5

2. Set up the division problem with 19 as the numerator and 5 as the denominator, placing the decimal point in the quotient above the division bar.

3.8
___________
5 | 19.00

3. Divide 19 by 5, which gives 3 as the quotient.

3.8
___________
5 | 19.00
15
___________
40

4. Multiply the quotient (3) by 5 and subtract from 19. Write the result (4) under the line.

3.8
___________
5 | 19.00
15
___________
40
- 40
___________
0

5. Since no more digits remain, the long division is complete.

In this case, the decimal representation of 3 4/5 is 3.8.

Answer 6

Use long division to convert 13/20 to a decimal.(1 point)

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Answer 7

[AI-generated answer — Bot GPT 3.5]

To convert the fraction 13/20 to a decimal using long division, follow these steps:

1. Set up the division problem with 13 as the numerator and 20 as the denominator, placing the decimal point in the quotient above the division bar.

0.
____
20 | 13.00

2. Divide 13 by 20, which gives 0 as the quotient.

0.
____
20 | 13.00
0

3. Multiply the quotient (0) by 20 and subtract from 13. Write the result (13) under the line.

0.
______
20 | 13.00
- 0
_______
13

4. Bring down the next digit (0) after the decimal point.

0.
______
20 | 13.00
- 0
_______
13
0

5. Divide 130 by 20, which gives 6 as the quotient.

0.6
______
20 | 13.00
- 0
_______
13
0
______
130

6. Multiply the quotient (0.6) by 20 and subtract from 130. Write the result (10) under the line.

0.6
______
20 | 13.00
- 0
_______
13
0
______
130

7. Since no more digits remain, the long division is complete.

In this case, the decimal representation of 13/20 is 0.65.

Answer 8

Use long division to convert 2/9 to a decimal. Your approximation should have one decimal place.(1 point)

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Answer 9

[AI-generated answer — Bot GPT 3.5]

To convert the fraction 2/9 to a decimal using long division and approximating to one decimal place, follow these steps:

1. Set up the division problem with 2 as the numerator and 9 as the denominator, placing the decimal point in the quotient above the division bar.

0.
____
9 | 2.0

2. Divide 2 by 9. Since 9 does not divide evenly into 2, add a decimal point and a zero to the right of the quotient.

0.
____
9 | 2.0
0

3. Multiply the quotient (0) by 9 and subtract from 2. Write the result (2) under the line.

0.
______
9 | 2.0
0
_______
2

4. Bring down the next digit (0) after the decimal point.

0.
______
9 | 2.0
0
_______
2
0

5. Divide 20 by 9. The result is approximately 2 with a remainder of 2. Write 2 as the next decimal place in the quotient.

0.2
______
9 | 2.0
0
_______
2
0
_______
20

6. Multiply the quotient (0.2) by 9 and subtract from 20. Write the result (2) under the line.

0.2
______
9 | 2.0
0
_______
2
0
_______
20

7. Since we are approximating to one decimal place, we stop here.

In this case, the decimal representation of 2/9 (approximated to one decimal place) is 0.2.

Answer 10

Use long division to convert 27/50 to a decimal.(1 point)

Answer 11

[AI-generated answer — Bot GPT 3.5]

To convert the fraction 27/50 to a decimal using long division, follow these steps:

1. Set up the division problem with 27 as the numerator and 50 as the denominator, placing the decimal point in the quotient above the division bar.

0.
_________
50 | 27.00

2. Divide 27 by 50, which gives 0 as the quotient.

0.
_________
50 | 27.00
0

3. Multiply the quotient (0) by 50 and subtract from 27. Write the result (27) under the line.

0.
_________
50 | 27.00
0
_________
27

4. Bring down the next digit (0) after the decimal point.

0.
_________
50 | 27.00
0
_________
27
0

5. Divide 270 by 50, which gives 5 as the quotient.

0.5
_________
50 | 27.00
0
_________
27
0
_________
270

6. Multiply the quotient (0.5) by 50 and subtract from 270. Write the result (20) under the line.

0.5
_________
50 | 27.00
0
_________
27
0
_________
270
- 250
_________
20

7. Bring down the next digit (0) after the decimal point.

0.54
_________
50 | 27.00
0
_________
27
0
_________
270
- 250
_________
20
0

8. Divide 200 by 50, which gives 4 as the quotient.

0.54
_________
50 | 27.00
0
_________
27
0
_________
270
- 250
_________
20
0
_________
200

9. Multiply the quotient (0.54) by 50 and subtract from 200. Write the result (40) under the line.

0.54
_________
50 | 27.00
0
_________
27
0
_________
270
- 250
_________
20
0
_________
200
- 200
_________
0

10. Since no more digits remain, the long division is complete.

In this case, the decimal representation of 27/50 is 0.54.

Answer 12

Use long division to convert 3 3/8 to a decimal.(1 point)

Answer 13

[AI-generated answer — Bot GPT 3.5]

To convert the mixed number 3 3/8 to a decimal using long division, follow these steps:

1. Convert the mixed number into an improper fraction. Multiply the whole number (3) by the denominator (8) and add the numerator (3). Write the sum (27) over the denominator.

3 3/8 = ((3 * 8) + 3) / 8 = 27/8

2. Set up the division problem with 27 as the numerator and 8 as the denominator, placing the decimal point in the quotient above the division bar.

3.
____
8 | 27.00

3. Divide 27 by 8, which gives 3 as the quotient.

3.
____
8 | 27.00
24
_______
30

4. Multiply the quotient (3) by 8 and subtract from 27. Write the result (3) under the line.

3.
______
8 | 27.00
24
_______
30
- 24
_______
6

5. Bring down the next digit (0) after the decimal point.

3.
______
8 | 27.00
24
_______
30
- 24
_______
6
0

6. Divide 60 by 8, which gives 7 as the quotient.

3.3
______
8 | 27.00
24
_______
30
- 24
_______
6
0
_______
60

7. Multiply the quotient (3.3) by 8 and subtract from 60. Write the result (4) under the line.

3.3
______
8 | 27.00
24
_______
30
- 24
_______
6
0
_______
60
- 56
_______
40

8. Bring down the next digit (0) after the decimal point.

3.37
______
8 | 27.00
24
_______
30
- 24
_______
6
0
_______
60
- 56
_______
40
32

9. Divide 320 by 8, which gives 4 as the quotient.

3.37
______
8 | 27.00
24
_______
30
- 24
_______
6
0
_______
60
- 56
_______
40
32
_______
320

10. Multiply the quotient (3.375) by 8 and subtract from 320. Write the result (0) under the line.

3.375
______
8 | 27.00
24
_______
30
- 24
_______
6
0
_______
60
- 56
_______
40
32
_______
320
- 320
_______
0

11. Since no more digits remain, the long division is complete.

In this case, the decimal representation of 3 3/8 is 3.375.

Answer 14

Use long division to convert 4/15 to a decimal.(1 point)

Answer 15

[AI-generated answer — Bot GPT 3.5]

To convert the fraction 4/15 to a decimal using long division, follow these steps:

1. Set up the division problem with 4 as the numerator and 15 as the denominator, placing the decimal point in the quotient above the division bar.

0.
_________
15 | 4.00

2. Divide 4 by 15. Since 15 does not divide evenly into 4, add a decimal point and a zero to the right of the quotient.

0.
_________
15 | 4.00
0

3. Multiply the quotient (0) by 15 and subtract from 4. Write the result (4) under the line.

0.
_________
15 | 4.00
0
_________
4

4. Bring down the next digit (0) after the decimal point.

0.
_________
15 | 4.00
0
_________
4
0

5. Divide 40 by 15. The result is approximately 2 with a remainder of 10. Write 2 as the next decimal place in the quotient.

0.2
_________
15 | 4.00
0
_________
4
0
_________
40

6. Multiply the quotient (0.2) by 15 and subtract from 40. Write the result (10) under the line.

0.2
_________
15 | 4.00
0
_________
4
0
_________
40
- 30
_________
10

7. Bring down the next digit (0) after the decimal point.

0.26
_________
15 | 4.00
0
_________
4
0
_________
40
- 30
_________
10
0

8. Divide 100 by 15. The result is approximately 6 with a remainder of 10. Write 6 as the next decimal place in the quotient.

0.26
_________
15 | 4.00
0
_________
4
0
_________
40
- 30
_________
10
0
_________
100

9. Multiply the quotient (0.26) by 15 and subtract from

Answer 16

Use long division to convert 7/11 to a decimal.(1 point)

Responses

≈1.571428
approximately equals 1.571428

63
63

≈0.63
approximately equals 0.63

7.11
7.11