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
yes
2 / 3 = 0.66666...
6 / 10 = 0.6
4 / 5 = 2 ∙ 4 / 2 ∙ 5 = 8 / 10 = 0.8
6 / 5 = 2 ∙ 6 / 2 ∙ 5 = 12 / 10 = 1.2
What do you think?
To find the rational number that equals 0.6̅ (which represents a repeating decimal), we can use a simple algebraic method.
Let x be the decimal number we are trying to find. To convert 0.6̅ to a fraction, we multiply it by 10 to shift the repeating part to the left of the decimal point:
10x = 6.6̅
Next, we subtract the original equation from the one with the repeating decimal shifted:
10x - x = 6.6̅ - 0.6̅
Simplifying:
9x = 6
Finally, we solve for x by dividing both sides of the equation by 9:
x = 6/9
Simplifying the fraction:
x = 2/3
Therefore, the rational number that equals 0.6̅ is 2/3.