Question

Convert 0.bar(8) into a rational number

Answer 1

To convert 0.bar(82) to a rational number, you would set x equal to 0.bar(82) and then multiply both sides of the equation by what number?

Answer 2

To convert the recurring decimal 0.bar(8) into a rational number, we can use algebraic manipulation.

Let x = 0.bar(8)
Multiply both sides of the equation by 10 to move the decimal point:
10x = 8.bar(8)

Subtracting the original equation from this new equation eliminates the recurring part:
10x - x = 8.bar(8) - 0.bar(8)
9x = 8

Divide both sides of the equation by 9:
x = 8/9

Therefore, 0.bar(8) is equivalent to the rational number 8/9.

Answer 3

To convert 0.bar(82) into a rational number, let's set x equal to 0.bar(82).

Since there are two digits in the recurring part (82), we need to multiply both sides of the equation by a power of 10 that will eliminate the recurring part.

In this case, we multiply by 100 because we want to move the decimal point two places to the right.

So, multiply both sides of the equation by 100:
100x = 82.bar(82)

Now, subtract the original equation from this new equation, which will eliminate the recurring part:
100x - x = 82.bar(82) - 0.bar(82)
99x = 82

Finally, divide both sides of the equation by 99:
x = 82/99

Therefore, 0.bar(82) is equivalent to the rational number 82/99.