Use long division to convert 2/9 to a decimal. Your approximation should have one decimal place.(1 point)
≈
0.2
To convert 2/9 to a decimal using long division, follow these steps:
1. Write 2 as the dividend and 9 as the divisor.
0.2 →
2. Divide the first digit of the dividend (2) by the divisor (9). Write the quotient above the division line.
0.2
____
9) 2
3. Multiply the quotient (0) by the divisor (9), and write the result below the dividend.
0.2
____
9) 2
0
4. Subtract the result from step 3 from the previous dividend (2).
0.2
____
9) 2
-0
5. Bring down the next digit from the dividend (0) and place it after the previous result.
0.2
____
9) 2
- 0
2
6. Divide the new dividend (20) by the divisor (9). Write the quotient above the division line.
0.2
____
9) 2
- 0
20
__
0
7. Multiply the quotient (2) by the divisor (9), and write the result below the new dividend (20).
0.2
____
9) 2
- 0
20
-18
__
2
8. Subtract the result from step 7 from the previous dividend (20).
0.2
____
9) 2
- 0
20
-18
__
2
9. Since the remainder (2) is less than the divisor (9), add a decimal point to the quotient and bring down a zero, then continue dividing.
0.2
____
9) 2.0
- 1.8
____
2
10. Divide the new dividend (20) by the divisor (9). Write the quotient above the division line.
0.2
____
9) 2.0
- 1.8
____
2
-1
__
1
11. Multiply the quotient (2) by the divisor (9), and write the result below the new dividend (20).
0.2
____
9) 2.0
- 1.8
____
2
-1
__
1
- 0.9
____
1
12. Subtract the result from step 11 from the previous dividend (20).
0.2
____
9) 2.0
- 1.8
____
2
-1
__
1
- 0.9
____
1
13. The remainder (1) is still greater than the divisor (9), so add a decimal point to the quotient and bring down a zero, then continue dividing.
0.2
____
9) 2.0
- 1.8
____
2
-1
__
1
- 0.9
____
1
- 0.9
____
10
14. Divide the new dividend (10) by the divisor (9). Write the quotient above the division line.
0.2
____
9) 2.0
- 1.8
____
2
-1
__
1
- 0.9
____
1
- 0.9
____
10
1
__
10
15. Multiply the quotient (1) by the divisor (9), and write the result below the new dividend (10).
0.2
____
9) 2.0
- 1.8
____
2
-1
__
1
- 0.9
____
1
- 0.9
____
10
9
____
10
16. Subtract the result from step 15 from the previous dividend (10).
0.2
____
9) 2.0
- 1.8
____
2
-1
__
1
- 0.9
____
1
- 0.9
____
10
9
____
10
17. Since the remainder (10) is greater than the divisor (9), you can continue dividing infinitely. However, since we need to approximate to one decimal place, we stop here.
Therefore, 2/9 as a decimal, rounded to one decimal place, is approximately 0.2.