To convert the fraction 2/9 to a decimal using long division, follow these steps:
1. Write the fraction as a division problem: 2 รท 9.
2. Perform the long division by dividing the numerator (2) by the denominator (9), and write the quotient above a horizontal line.
3. Place a decimal point in the quotient above the division line.
4. Continue by bringing down a zero next to the remainder, which is 2.
5. Divide the new dividend (20) by the denominator (9) and write the new quotient above the line.
6. Repeat the process of bringing down a zero next to the remainder (20) and dividing it by 9.
7. Continue this process until you find a repeating pattern or reach the desired level of precision (one decimal place).
Let's go through it step by step:
Step 1: Write the division problem: 2 รท 9.
0.
----
9 ) 2
Step 2: Divide 2 by 9, which equals 0 as a whole number. Write the 0 above the line and the remainder (2) on the right side.
0.
----
9 ) 2
Step 3: Place a decimal point above the division line.
0.
----
9 ) 2
Step 4: Bring down a zero next to the remainder (2) to create the new dividend (20).
0.
----
9 ) 2.0
Step 5: Divide 20 by 9, which equals 2 as a whole number. Write the 2 above the line.
0.2
----
9 ) 2.0
Step 6: Multiply 2 (quotient) by 9 (denominator) to get 18. Subtract 18 from 20 to find the remainder, which is 2.
0.2
----
9 ) 2.0
-18
---
2
Step 7: Bring down another zero next to the remainder (2) to create the new dividend (20).
0.2
----
9 ) 2.0
-18
---
20
Step 8: Divide 20 by 9, which equals 2 as a whole number. Write the 2 above the line.
0.2
----
9 ) 2.0
-18
---
20
-18
---
2
Now, we can see that the remainder is the same as we had before. Thus, 2/9 as a decimal is approximately 0.2 (rounded to one decimal place).