Question

Use long division to convert 2/9 to a decimal

Answer 1

[AI-generated answer — Bot GPT 3.5]

To convert 2/9 to a decimal using long division, follow these steps:

Step 1: Set up the long division problem:
Place the decimal point in the quotient directly above the division symbol.

0.
------
9| 2

Step 2: Divide:
Divide the first digit of the dividend (2) by the divisor (9). Place the quotient (2 ÷ 9) above the division symbol.

0.2
------
9| 2

Step 3: Multiply:
Multiply the divisor (9) by the quotient (2). Write the result below the dividend.

18
0.2
------
9| 2

Step 4: Subtract:
Subtract the product (18) from the first digit of the dividend (20). Write the result beneath the line.

18
0.2
------
9| 2
-18

Step 5: Bring down the next digit:
Bring down the next digit from the dividend (0) and write it next to the difference (2).

18
0.2
------
9| 2
-18
20

Step 6: Repeat:
Divide the new number (20) by the divisor (9). Place the quotient (2 ÷ 9) above the division symbol.

18
0.2 2
------
9| 2
-18
20

Step 7: Multiply:
Multiply the divisor (9) by the quotient (2). Write the result below the new number.

18
0.2 2
------
9| 2
-18
20
18

Step 8: Subtract:
Subtract the product (18) from the new number (20). Write the result beneath the line.

18
0.2 2
------
9| 2
-18
20
-18

Step 9: Bring down the next digit:
Since the dividend has a remainder of 2 and no more digits, the process stops here.

Step 10: Final result:
The decimal equivalent of 2/9 is 0.2 recurring, which can be represented as 0.2̅ or 0.2 overlined.

Answer 2

[AI-generated answer — Step-by-Step Bot]

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

1. Write down the fraction 2/9.
2. Divide the numerator (2) by the denominator (9). The result is the whole number part of the decimal.
- 2 ÷ 9 = 0 (whole number part)
3. Write down a decimal point (.) and a zero next to it.
- 0.
4. Bring down a zero after the zero from the previous step to create a remainder of 0.
- 0.0
5. Divide the remainder (0) by the denominator (9), and write down the result after the decimal point.
- 0 ÷ 9 = 0 (the first decimal place)
- Write down 0 after the decimal point.
- 0.0
6. Repeat step 5 until the desired level of accuracy is achieved or a repeating pattern is detected.
- Since the remainder is still 0, the decimal ends here.
7. The final result is 0.2 recurring in decimal notation, which can also be written as 0.2̅.
- 2/9 as a decimal = 0.2̅

Therefore, the decimal equivalent of the fraction 2/9 is 0.2 recurring or 0.2̅.