Convert 0.09 (with a bar notation over 09) to a rational number in simplest form.
To convert a decimal number with a bar notation to a rational number in simplest form, we can follow these steps:
Let x = 0.090909...
Multiply x by 100 to remove the bar notation:
100x = 9.090909...
Subtract x from 100x:
100x - x = 9.090909... - 0.090909...
99x = 9
Divide both sides of the equation by 99:
x = 9/99
Simplify the fraction:
x = 1/11
Therefore, the rational number equivalent to 0.09 (with a bar notation over 09) in simplest form is 1/11.
To convert the decimal number 0.09 with a bar notation over 09 to a rational number in simplest form, we can follow these steps:
Step 1: Let x be the repeating decimal, then multiply x by 100 to remove the bar notation.
100x = 9.090909...
Step 2: Subtract x from 100x to eliminate the repeating part.
100x - x = 9.090909... - 0.090909...
Simplifying the right side of the equation gives:
99x = 9.
Step 3: Divide both sides of the equation by 99 to solve for x.
99x/99 = 9/99
x = 9/99
Step 4: Simplify the fraction 9/99 to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).
GCD(9, 99) = 9
Simplifying 9/99:
9 ÷ 9 / 99 ÷ 9
1/11
Therefore, the rational representation of 0.09 with a bar notation over 09 is 1/11 in its simplest form.