Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
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0.72¯¯¯¯¯ can be represented as the infinite decimal 0.727272...
Let x = 0.727272...
Then, 100x = 72.727272...
Subtracting x from 100x, we get:
(100x - x) = (72.727272... - 0.727272...)
99x = 72
Dividing both sides by 99:
x = 72/99
This rational number can be simplified further by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = (72/9) / (99/9)
x = 8/11
Therefore, 0.72¯¯¯¯¯ can be represented as the rational number 8/11 in simplest form.
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
311
Start Fraction 3 over 11 end fraction
27100
Start Fraction 27 over 100 end fraction
127
Start Fraction 1 over 27 end fraction
2799
To convert a recurring decimal to a rational number in simplest form, we can use a basic algebraic method.
Let's represent the recurring decimal 0.72¯¯¯¯¯ as x.
To remove the recurring part, we can multiply both sides of the equation by a power of 10 that will eliminate the recurring part.
Since there are two decimal places in the recurring part, let's multiply both sides by 100 (10^2):
100x = 72.7272¯¯¯¯¯
Next, we can subtract the original equation from the equation obtained by multiplying by 100:
100x - x = 72.7272¯¯¯¯¯ - 0.72¯¯¯¯¯
Simplifying:
99x = 72.0072¯¯¯¯¯
Now, we need to isolate x. We can divide both sides of the equation by 99:
99x / 99 = 72.0072¯¯¯¯¯ / 99
Simplifying:
x = 0.727272¯¯¯¯¯
So the rational number representation of 0.72¯¯¯¯¯ in simplest form is 0.7272.
To convert a recurring decimal like 0.72¯¯¯¯¯ to a rational number in simplest form, we need to represent it as a fraction.
Let's call the number 0.72¯¯¯¯¯ as "x".
To get rid of the recurring decimal, we can multiply x by a power of 10 that will shift the recurring part to the left of the decimal point. We want to shift the recurring part in 0.72¯¯¯¯¯ (which is the 72) to the left, so we multiply both sides of the equation by 100:
100x = 72.72¯¯¯¯¯
Next, let's subtract the original equation from the new equation to eliminate the recurring part:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Now, we can simplify the fraction by dividing both sides of the equation by the greatest common divisor (GCD) of 99 and 72, which is 9:
99x/9 = 72/9
11x = 8
Finally, divide both sides of the equation by 11 to isolate x:
11x/11 = 8/11
x = 8/11
Therefore, the rational number equivalent of 0.72¯¯¯¯¯ in simplest form is 8/11.