We want to find the probability that an athlete makes a half-court shot, given the probability of making a three-quarter-court shot. The probability of making the half-court shot is 22 times greater than the probability of making the three-quarter-court, which is 0.009. Let's start by rewriting the given repeating decimal as a fraction by following these three steps.
Write the equation x=d, where d is a repeating decimal.
Subtract the equation from the previous step from the equation 10^n x=10^n d, where n is the number of repeating digits.
Solve the equation for x.
We can use this process to rewrite 0.009 as a fraction. We substitute 0.009 for d and 1 for n, as there is only one repeating digit in the decimal.
ccc x=d & ⇔ & x= 0.009 10^nx=10^n d & ⇔ & 10^1x=10^1( 0.009)
Let's simplify the second equation.
10^1x=10^1(0.009) ⇒ 10x=0.09
Now we are ready to subtract the first equation from the second one.
c r c l& 10x & = & 0.09 -( & x & = & 0.009 ) & 9x & = & 0.09
Finally, we can solve for x. Let's do it!
The probability the athlete makes a three-quarter-court shot is 1100. From the exercise, we know that the athlete is 22 times more likely to make a half-court than a three-quarter-court shot. Let's multiply 1100 by 22 to find the probability of making a half-court shot.
1/100* 22= 22/100
A percent can be expressed as a fraction over 100, so we do not need to make any further calculations — we can just write the answer as a percent.
22/100=22 %
