Convert 0.8 to a rational number.
(Bar notation over 8)
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.
Wrong
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.
To convert 0.8 to a rational number with bar notation over 8, we can rewrite it as a fraction. Let's multiply both sides of the equation by 100 to get rid of the decimal point:
0.8 * 100 = 80
Now, we have 80/100 as a fraction. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 20:
80 ÷ 20 /100 ÷ 20 = 4/5
Therefore, 0.8 with bar notation over 8 can be written as the rational number 4/5.