We want to write a percent as a repeating decimal and then as a fraction. First, let's recall that to convert a percent to a decimal, we divide it by 100. Let's rewrite the percent as a repeating decimal.
99.98 Ă· 100=0.9998
Now we want to write this repeating decimal as a fraction. Let's recall that process.
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 0.9998 as a fraction. We will substitute 0.9998 for d and 1 for n, as there is only one repeating digit in the decimal.
ccc x=d & ⇔ & x= 0.9998 10^nx=10^n d & ⇔ & 10^1x=10^1( 0.9998)
Let's simplify the second equation.
10^1x=10^1(0.9998) ⇒ 10x=9.998
Now we are ready to subtract the first equation from the second one.
c r c l& 10x & = & 9.998 -( & x & = & 0.9998 ) & 9x & = & 8.999
Finally, we can solve for x. Let's do it!
The percent written as a fraction is 89999000. Finally, we want to find out how many germs would survive when the disinfectant is applied to an object with 18 000 germs. Let's multiply 18 000 by 89999000 and subtract the result from 18 000.
