Asked by Gelo

Convert 0.8 to a rational number.
(Bar notation over 8)
Answered by Gelo
Wrong
Answered by GPT 3.5
To write 0.8 with a bar notation over 8, we need to re-write it as a fraction.

Let x = 0.8 (with a bar notation over 8)

To remove the bar notation, we multiply both sides of the equation by a power of 10 that will shift the repeating decimal part to the left of the decimal point. Since the bar is only over the 8, we multiply by 10.

10x = 8.888...

Now, subtract x from both sides of the equation to eliminate the repeating part.

10x - x = 8.888... - 0.8
9x = 8.088...

To simplify the repeating decimal, set it equal to y.

y = 0.088...

Now, multiply y by 100 to shift the repeating part to the left of the decimal point.

100y = 8.888...

Now, subtract y from both sides of the equation to eliminate the repeating part.

100y - y = 8.888... - 0.088...
99y = 8.8

Now, divide both sides of the equation by 99 to solve for y.

y = 8.8/99
y = 0.088

Substitute the value of y back into the original equation to solve for x.

9x = 8.088...
9x = 8 + 0.088
9x = 8.088
x = 8.088/9
x ≈ 0.898

Therefore, 0.8 (with a bar notation over 8) can be written as the rational number 0.898 or approximately 0.898.
Answered by GPT 3.5
My apologies for the mistake. To convert 0.8 to a rational number with a bar notation over 8, we can represent it as 0.8 with an 8 repeated infinitely.

Let x = 0.8 (with a bar notation over 8)
Multiply both sides of the equation by 10 to shift the repeating part to the left of the decimal point:
10x = 8.888...

Now, subtract x from both sides to eliminate the repeating part:
10x - x = 8.888... - 0.8
9x = 8.088...

Simplify the repeating decimal by setting it equal to y:
y = 0.088...

Multiply y by 100 to shift the repeating part to the left of the decimal point:
100y = 8.888...

Subtract y from both sides to eliminate the repeating part:
100y - y = 8.888... - 0.088...
99y = 8.8

Solve for y by dividing both sides by 99:
y = 8.8/99
y = 0.088

Substitute the value of y back into the original equation to solve for x:
9x = 8.088...
x = 8.088/9
x = 0.898666...

Therefore, 0.8 (with a bar notation over 8) can be written as the rational number 0.898666... or approximately 0.898666.