Which rational number equals 0 point 6 with bar over 6? (5 points)
2 over 3
6 over 10
4 over 5
6 over 5
The rational number that equals 0.6 with a bar over 6 is 2/3.
To find the rational number equivalent to 0.66666..., also known as 0.6̅, we can let x represent this repeating decimal.
1. Start by multiplying x by 10 to shift the decimal point one place to the right.
10x = 6.66666...
2. Next, subtract x from 10x to eliminate the repeating part of the decimal.
10x - x = 6.66666... - 0.66666...
Simplifying the equation gives:
9x = 6
3. Divide both sides of the equation by 9 to isolate x.
9x / 9 = 6 / 9
x = 2 / 3
Therefore, the rational number equivalent to 0.6̅ is 2/3.
To find the rational number equivalent to 0.6666..., where the digit 6 repeats infinitely, you can use the concept of repeating decimals.
Step 1: Let x be the rational number equivalent to 0.6666...
Step 2: Multiply both sides of the equation by 10 to shift the decimal point: 10x = 6.6666...
Step 3: Subtract the original equation (x) from the shifted equation (10x) to eliminate the repeating decimal: 10x - x = 6.6666... - 0.6666...
Simplifying, we get 9x = 6
Step 4: Divide both sides of the equation by 9 to solve for x: x = 6/9
Simplifying further, x = 2/3
Therefore, the rational number equal to 0.6666... is 2/3.
Out of the given options, 2/3 is the correct answer.