Bot GPT 3.5
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Bot GPT 3.5
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
To convert a recurring decimal like 0.72¯¯¯¯¯ to a rational number, we can use the concept of geometric series. Let x = 0.72¯¯¯¯¯, then 100x = 72.72¯¯¯¯¯.
Subtracting these two equations, we get:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
x = 72/99
Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:
(72/9) / (99/9) = 8/11
Therefore, the rational number equivalent to 0.72¯¯¯¯¯ in simplest form is 8/11.
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To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the following steps:
Step 1: Let x = 0.72¯¯¯¯¯
Step 2: Multiply both sides of the equation by 100 (since there are two decimal places in the repeating part).
100x = 72.72¯¯¯¯¯
Step 3: Subtract the original equation from the new equation to eliminate the repeating part.
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Step 4: Divide both sides of the equation by 99 to solve for x.
x = 72/99
Step 5: Simplify the fraction if possible.
x = 8/11
Therefore, the rational number equivalent to 0.72¯¯¯¯¯ is 8/11 in its simplest form.
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, follow these steps:
1. Let x = 0.72¯¯¯¯¯.
2. Multiply both sides of the equation by 100 to get rid of the repeating decimal:
100x = 72.72¯¯¯¯¯.
3. Subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯.
Simplifying it, we get:
99x = 72.
4. Divide both sides of the equation by 99 to solve for x:
x = 72 / 99.
Now we have converted the repeating decimal 0.72¯¯¯¯¯ to the fraction 72/99. To simplify this fraction:
1. Find the greatest common divisor (GCD) of the numerator and denominator, which in this case is 9.
2. Divide both the numerator and denominator by the GCD:
(72 ÷ 9) / (99 ÷ 9) = 8/11.
Therefore, the simplest form of 0.72¯¯¯¯¯ is 8/11.