Use long division to convert 5 3 to a decimal. (1 point)
16
To convert 5/3 to a decimal using long division, follow these steps:
1. Write the fraction as a division problem: 5 รท 3.
1 ______
3 | 5
2. Divide the numerator (5) by the denominator (3), using long division:
1 ______
3 | 5
-3
---
2
3. Since we reach a remainder of 2, bring down the next digit, which is a 0.
1 ______
3 | 5
-3
---
20
4. Divide 20 by 3:
1 ______
3 | 5
-3
---
20
- 18
---
2
5. This process can continue indefinitely, but for the purpose of converting to a decimal, you might choose to stop after a set number of decimal places. For example, let's say we want to stop after 4 decimal places.
1 ______
3 | 5.0000
-3
---
20
- 18
---
20
- 18
---
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
20
- 18
-----
0
6. After performing long division, we get the decimal form of 5/3 as approximately 1.6666.
Therefore, 5/3 as a decimal is approximately 1.6666.
To convert the fraction 5/3 to a decimal using long division, follow these steps:
1. Write down the numerator (5) as the dividend and the denominator (3) as the divisor.
____
3|5
2. Divide the first digit of the dividend (5) by the divisor (3). Write the quotient (1) above the line.
1
____
3|5
3. Multiply the divisor (3) by the quotient (1) and write the result (3) below the dividend.
1
____
3|5
-3
4. Subtract the result (3) from the dividend (5) and write the new value (2) below the line.
1
____
3|5
-3
2
5. Bring down the next digit from the dividend (0) and append it to the current value (2) to get a new dividend of 20.
1
____
3|50
-3
20
6. Divide the new dividend (20) by the divisor (3) to get the next digit of the quotient. Write the quotient (6) above the line.
16
____
3|50
-3
20
-18
7. Multiply the divisor (3) by the new quotient (6) and write the result (18) below the new dividend.
16
____
3|50
-3
20
-18
18
8. Subtract the result (18) from the new dividend (20) and write the new value (2) below the line.
16
____
3|50
-3
20
-18
18
2
9. Since there are no more digits to bring down, and the remainder (2) is not zero, add a decimal point at the end of the quotient and continue the process with a new dividend of 20.
16.1
____
3|50
-3
20
-18
18
2
10. Bring down a zero from the dividend and append it to the current value (2) to get a new dividend of 20.
16.1
____
3|500
-3
20
-18
18
2
11. Divide the new dividend (200) by the divisor (3) to get the next digit of the quotient. Write the quotient (6) above the line.
16.16
____
3|500
-3
20
-18
18
2
18
12. Multiply the divisor (3) by the new quotient (6) and write the result (18) below the new dividend.
16.166
____
3|500
-3
20
-18
18
2
18
18
13. Subtract the result (18) from the new dividend (20) and write the new value (2) below the line.
16.166
____
3|500
-3
20
-18
18
2
18
18
2
14. Since there are no more digits to bring down, and the remainder (2) is not zero, add a decimal point at the end of the quotient and continue the process with a new dividend of 20.
16.1666
____
3|500
-3
20
-18
18
2
18
18
2
15. Keep repeating steps 10 to 14 until you have enough decimal places or a repeating pattern emerges. In this case, it becomes apparent that the remainder (2) repeats at each step.
Therefore, the fraction 5/3, when converted to a decimal using long division, is approximately 1.666 recurring, or 1.6666... as an infinite decimal.