The decimal representation of the ration number 8 by 27 is 0.29629629629

Decimal representation of rational number 8/27

To find the decimal representation of the rational number 8/27, we need to divide the numerator (8) by the denominator (27) using long division.

Step 1: Set up the division problem

To start, we write the numerator (8) inside the division bracket and the denominator (27) outside the bracket.

_______
27 | 8

Step 2: Divide the first digit

We divide the first digit of the numerator (8) by the denominator (27). Since 8 is less than 27, we add a decimal point after the 8 and put a zero after the decimal point.

_______
27 | 8.0

Step 3: Multiply and subtract

Next, we multiply the denominator (27) by the quotient digit (0) and subtract it from the numerator (8). The result is then written below the line.

_______
27 | 8.0
- 0

The new numerator becomes 8. We bring down the next digit (0) from the decimal part.

Step 4: Bring down the next digit

We bring down the next digit (0) from the decimal part and divide it by the denominator (27). Since 0 is less than 27, we add a zero after the decimal point.

_______
27 | 8.00
- 0

Step 5: Multiply and subtract

We multiply the denominator (27) by the quotient digit (0) and subtract it from the numerator (0). The result is then written below the line.

_______
27 | 8.00
- 0
-----
0

The new numerator becomes 0. We bring down the next digit (0) from the decimal part.

Step 6: Bring down the next digit

We bring down the next digit (0) from the decimal part and divide it by the denominator (27). Since 0 is less than 27, we add a zero after the decimal point.

_______
27 | 8.000
- 0
-----
0

Step 7: Multiply and subtract

We multiply the denominator (27) by the quotient digit (0) and subtract it from the numerator (0). The result is then written below the line.

_______
27 | 8.000
- 0
-----
0

The new numerator becomes 0. Since the numerator is now 0, we can stop the long division process.

Step 8: Final decimal representation

The decimal representation of the rational number 8/27 is 0.296296... (the digits 296 keep repeating). This can also be written as 0.2̅9̅6̅.

Therefore, the decimal representation of the rational number 8/27 is 0.296296... or 0.2̅9̅6̅.

0.29629629