Use long division to convert 2/9 to a decimal
To convert the fraction 2/9 to a decimal using long division, follow these steps:
1) Write the fraction as a division problem: divide 2 by 9.
- Place 2 as the dividend (the number being divided)
- Place 9 as the divisor (the number doing the dividing)
0.____
9 | 2
2) Begin the long division process by dividing the first digit of the dividend (in this case, 2) by the divisor (9). Write the quotient above the line.
- 2 ÷ 9 = 0.2
0.2___
9 | 2
3) Multiply the quotient (0.2) by the divisor (9) and subtract the result from the dividend (2).
- 2 - (0.2 × 9) = 2 - 1.8 = 0.2
0.2___
9 | 2.0
4) Bring down the next digit of the dividend, which is 0, and place it to the right of the previous remainder (0.2).
- Resulting dividend: 0.20
0.2___
9 | 2.0
5) Divide the new dividend (0.20) by the divisor (9), obtaining a new quotient.
- 0.20 ÷ 9 = 0.02222222... (repeating decimal)
0.2___
9 | 2.0
6) The decimal starts to repeat, indicating that the division process will continue indefinitely. To display this repeating decimal form, we can use a vinculum (a horizontal line placed above the repeating pattern), as follows:
0.2___
9 | 2.0
-1.8
-----
0.20
-18
-------
0.0222...
Therefore, the fraction 2/9, when converted to a decimal using long division, is approximately 0.0222... (repeating).
To convert a fraction into a decimal, you can use long division. Here's how:
Step 1: Write the fraction as a division problem. In this case, the fraction is 2/9, so you would write 2 ÷ 9.
Step 2: Perform the long division. Start by dividing 2 by 9. The divisor, 9, goes into the first digit of the dividend, 2, 0 times. Write 0 above the division line.
0
------
9 ) 2
Step 3: Bring down the next digit of the dividend. In this case, there are no more digits. Since we're looking for the decimal representation, we need to add a decimal point after the dividend and bring down a zero.
0.
------
9 ) 20
Step 4: Continue the division. Divide 20 by 9. The divisor, 9, goes into 20 twice. Write 2 above the division line.
0.2
------
9 ) 20
-18
----
20
Step 5: Subtract the product of the divisor (9) and quotient (2) from the dividend (20). Write the result below the line.
0.2
------
9 ) 20
-18
----
20
-18
----
2
Step 6: Bring down the next digit of the dividend. In this case, there are no more digits. Since we're looking for the decimal representation, we need to add a decimal point after the dividend and bring down another zero.
0.2
------
9 ) 20.0
-18
----
20
-18
----
20
Step 7: Continue the division. Divide 20 by 9. The divisor, 9, goes into 20 twice. Write 2 above the line.
0.2
------
9 ) 20.0
-18
----
20
-18
----
20
20
---
2
Step 8: Subtract the product of the divisor (9) and quotient (2) from the dividend (20). Write the result below the line.
0.2
------
9 ) 20.0
-18
----
20
-18
----
20
20
---
2
-18
-----
20
Step 9: Bring down the next digit of the dividend. In this case, there are no more digits. Since we're looking for the decimal representation, we need to add a decimal point after the dividend and bring down another zero.
0.2
------
9 ) 20.0
-18
----
20
-18
----
20
20
---
2
-18
-----
20
20
---
2
-
Step 10: Since we have a repeating decimal pattern (0.2), 2 ÷ 9 can be expressed as 0.2 with a bar over the 2: 0.2̅.
To convert a fraction to a decimal using long division, follow these steps:
Step 1: Write down the fraction as a division problem, with the numerator inside the division symbol (÷) and the denominator outside the division symbol.
In this case, you would write 2 ÷ 9.
Step 2: Begin by dividing the numerator (2) by the denominator (9).
2 divided by 9 equals 0 with a remainder of 2.
Step 3: Bring down a zero after the remainder.
The division becomes 20 ÷ 9.
Step 4: Divide the new numerator (20) by the denominator (9).
20 divided by 9 equals 2 with a remainder of 2.
Step 5: Repeat the process by bringing down a zero and dividing the new numerator (20) by the denominator (9) again.
The division becomes 20 ÷ 9.
Step 6: Continue this process until you get the desired level of accuracy or until you notice a pattern in the decimal.
In this case, you can see that the remainder will always be 2. Thus, the decimal representation of 2/9 is 0.2222... (the pattern continues indefinitely with 2 repeating).
Therefore, 2/9 as a decimal is approximately 0.2222... or simply 0.2 with the repeating digit 2.
Note: If you want a decimal approximation with a specific number of decimal places, you can end the division process after that many decimal places.