Convert 0.72 72 72 to a rational number in the simplest form
0.727272... can be converted to a rational number by expressing it as a fraction. Since the digits 72 repeat infinitely, we can use the property of repeating decimals to convert it to a fraction.
Let's call the repeating fraction x. To convert it to a fraction, we multiply it by a power of 10 that eliminates the repeating part. In this case, we multiply it by 100 to remove the repeating part:
0.727272... * 100 = 72.727272...
Now, we subtract the original decimal from the multiplied decimal:
100x - x = 72.727272... - 0.727272...
99x = 72
To find x, we divide both sides of the equation by 99:
x = 72/99
The fraction 72/99 can be simplified. Both 72 and 99 can be divided by 9:
72/9 = 8
99/9 = 11
So, the simplified fraction is:
x = 8/11
Therefore, 0.727272... can be expressed as a rational number in simplest form as 8/11.
To convert 0.72 72 72 to a rational number in the simplest form, we first need to understand the pattern.
Looking at the number, we can observe that it has a repetitive pattern after the decimal point. The pattern starts from the second decimal place and repeats every two decimal places. So, we can represent the number as follows:
0.727272...
To convert this to a rational number, let's call it x, we need to multiply it by a power of 10 to eliminate the repeating decimal. Since the pattern repeats every two decimal places, we can multiply it by 100 to shift the decimal point two places to the right:
100x = 72.727272...
Now, we can subtract x from 100x to eliminate the repeating part:
100x - x = 72.727272... - 0.727272...
99x = 72
Dividing both sides by 99, we get:
x = 72/99
To simplify this fraction, we can find the greatest common divisor (GCD) of the numerator and denominator, which is 9. Dividing both the numerator and denominator by 9:
x = (72/9) / (99/9)
x = 8/11
Therefore, 0.72 72 72 as a rational number in the simplest form is 8/11.
To convert a decimal number to a rational number, we need to express it as a fraction with integers in the numerator and the denominator.
In this case, the decimal number is 0.727272...
Let's call this decimal number x. So, x = 0.727272...
Now, we can multiply x by a power of 10 to eliminate the repeating decimal part.
Multiply x by 100 (since there are at least two digits repeating):
100x = 72.727272...
Now, subtract the original x from this equation to eliminate the repeating part:
100x - x = 72.727272... - 0.727272...
99x = 72
Divide both sides by 99:
x = 72/99
This is a rational number in the form of a fraction. However, it is not in its simplest form yet.
To simplify this fraction, we can find the greatest common divisor (GCD) of the numerator and denominator, and divide both by this GCD.
In this case, the GCD of 72 and 99 is 9.
Dividing 72 and 99 by 9:
72/9 = 8
99/9 = 11
Therefore, the simplest form of the rational number 0.727272... is 8/11.