Malik has a batting average of 0.81 repeating
. Write his batting average as a fraction in simplest form
To convert a repeating decimal to a fraction, we can use the following steps:
Let x be the repeating decimal.
Multiply x by 10 raised to the power of the number of digits in the repeating part (which in this case is 2) to eliminate the repeating part.
Subtract the original number (x) from the result obtained in step 2 to eliminate the non-repeating part.
In this case, let's follow these steps:
Let x = 0.81
Multiply x by 10² (since there are two repeating digits) to eliminate the repeating part: x * 10² = 81.81
Subtract the original number (0.81) from 81.81: 81.81 - 0.81 = 81
Now, we have the equation: 81 = 100x
Divide both sides of the equation by 100: x = 81/100
Simplifying the fraction, we find that Malik's batting average can be written as 81/100 in simplest form.
To convert Malik's batting average of 0.81 repeating to a fraction in simplest form, we can follow these steps:
Step 1: Let x be the repeating part of the decimal, which in this case is 81.
Step 2: Determine the denominator. Since there are two digits in the repeating part (81), we place the repeating part over a number consisting of two nines (99).
Step 3: Write the fraction using the repeating part over the denominator: x/99.
Step 4: Simplify the fraction by finding the greatest common divisor (GCD) of both the numerator and denominator and dividing both by it.
In this case, the numerator (x) is 81, and the denominator is 99. We can simplify 81/99 by dividing both numbers by their GCD, which is 9.
Dividing 81 by 9 gives us 9, and dividing 99 by 9 gives us 11.
Therefore, the simplified fraction for Malik's batting average of 0.81 repeating is 9/11.
To write Malik's batting average as a fraction in simplest form, we need to convert the repeating decimal into a fraction.
Let's denote Malik's batting average as a decimal x, which repeats indefinitely. To eliminate the repeating decimal, we can multiply x by a power of 10 equal to the number of repeating digits.
Since the digit 8 repeats, we can multiply x by 100, which will shift the decimal point two places to the right.
0.81 repeating * 100 = 81.81 repeating
Now, let's subtract the original equation from the equation above to eliminate the repeating part:
81.81 repeating - 0.81 repeating = 81
x * 100 - x = 81
99x = 81
To isolate x, divide both sides of the equation by 99:
99x / 99 = 81 / 99
x = 81 / 99
Since 81 and 99 are both divisible by 9, we can simplify the fraction:
x = (81 / 9) / (99 / 9)
x = 9 / 11
So Malik's batting average, written as a fraction in simplest form, is 9/11.