Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number, we can call it x. Then, we multiply x by a power of 10 to remove the repeating decimal. Let's multiply x by 100:
100x = 72.72¯¯¯¯¯
Next, we subtract x from 100x:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Dividing both sides of the equation by 99, we get:
x = 72/99
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 9:
x = (72/9) / (99/9)
x = 8/11
Therefore, the rational number equivalent to 0.72¯¯¯¯¯ is 8/11 in simplest form.
wait nvm i answered question before with 0.72¯¯¯¯¯, i shouldve wrote that instead.
No problem! To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can call it x. Then, we can multiply x by a power of 10 to eliminate the repeating decimal. Since there are two repeating digits, we'll multiply x by 100:
100x = 72.72¯¯¯¯¯
Next, we subtract x from 100x:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Now, divide both sides of the equation by 99:
x = 72/99
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 9:
x = (72/9) / (99/9)
x = 8/11
Therefore, the rational number equivalent to 0.72¯¯¯¯¯ is 8/11 in simplest form.
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the method of repeating decimals.
Let's represent 0.72¯¯¯¯¯ as x. By multiplying both sides of the equation by 100 (to move the decimal point two places to the right), we get:
100x = 72.72¯¯¯¯¯
Next, subtracting x from 100x, we have:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
To find the simplest form of the rational number, we divide both sides of the equation by 99:
99x / 99 = 72 / 99
x = 8/11
Therefore, the rational number equivalent to 0.72¯¯¯¯¯ in simplest form is 8/11.
To convert a repeating decimal into a rational number in simplest form, you can use the method of fractions. Here's how:
Step 1: Let x be the repeating decimal, in this case, x = 0.72¯¯¯¯¯.
Step 2: Multiply both sides of the equation by a power of 10 that is equal to the number of digits in the repeating part. In this case, there are 2 repeating digits (72), so we multiply both sides by 100:
100x = 72.7272¯¯¯¯¯
Step 3: Subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 72.7272¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Step 4: Solve for x by dividing both sides of the equation by 99:
x = 72/99
Step 5: Simplify the fraction. Both the numerator and denominator are divisible by 9:
x = (8 * 9)/(11 * 9) = 8/11
Therefore, the rational number equivalent to 0.72¯¯¯¯¯ in simplest form is 8/11.