To convert 0.264¯¯¯¯¯¯¯¯ to a rational number
To convert the repeating decimal 0.264¯¯¯¯¯¯¯¯ to a rational number, we can use the method of fractions.
Let's assign a variable, x, to our repeating decimal: x = 0.264¯¯¯¯¯¯¯¯
To eliminate the repeating part of the decimal, we can multiply both sides of the equation by 1000 (since there are three digits in the repeating part):
1000x = 264.264¯¯¯¯¯¯¯¯
Next, we subtract the original equation from the equation multiplied by 1000 to eliminate the repeating part:
1000x - x = 264.264¯¯¯¯¯¯¯¯ - 0.264¯¯¯¯¯¯¯¯
999x = 264
Finally, we solve for x by dividing both sides of the equation by 999:
x = 264/999
Therefore, the rational number equivalent to 0.264¯¯¯¯¯¯¯¯ is 264/999.
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
Responses
999
999
100
100
1,000
1,000
10
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by 1,000.
To convert a repeating decimal like 0.264¯¯¯¯¯¯¯¯ to a rational number, we can use algebraic manipulation.
Let's assume that x = 0.264¯¯¯¯¯¯¯¯.
To remove the repeating part, we can multiply both sides of the equation by a suitable power of 10. Since there are three digits in the repeating part (264), we can multiply by 1000.
1000x = 264.264¯¯¯¯¯¯¯¯ [Step 1]
Next, we can subtract the original equation from Step 1 to eliminate the repeating part.
1000x - x = 264.264¯¯¯¯¯¯¯¯ - 0.264¯¯¯¯¯¯¯¯
Simplifying, we get:
999x = 264
Now, divide both sides by 999 to solve for x:
x = 264 / 999
To simplify this fraction, we can find the greatest common divisor (GCD) of the numerator and denominator, which is 33.
So, the simplified fraction is:
x = (264/33) / (999/33) = 8/33
Therefore, the rational equivalent of 0.264¯¯¯¯¯¯¯¯ is 8/33.