We want to find how many units of the local currency our friend will receive when she gives the bank $ 200. To do so, we will rewrite the given repeating decimal as a fraction and then multiply it by the number of dollars left to exchange. First, let's recall how to write a repeating decimal as a fraction.
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 1.265 as a fraction. We will substitute 1.265 for d and 2 for n, as there are two repeating digits in the decimal number.
ccc
x=d & ⇔ & x= 1.265
10^n x=10^n d & ⇔ & 10^2 x=10^2( 1.265)
Let's simplify the second equation.
10^2x=10^2(1.265) ⇒ 100x=126.565
Now we are ready to subtract the first equation from the second one.
c r c l& 100x & = & 126.565 -( & x & = & 1.265 ) & 99x & = & 125.3
Finally, we can solve for x. Let's do it!
The exchange rate is 1253990. This means that for each dollar our friend gives to the bank, she will receive 1253990 units of local currency. Now, remember that the bank charges a $2 fee to change currency. Let's find how much of our friend's $200 will be converted into the local currency.
200-2=198
If our friend gives the bank $200, she will only be able to convert $198 to local currency. Finally, let's find out how many units of local currency this is by multipling 198 by 1253990.
198* 1253/990 = 248 094/990 = 250.6
Our friend will receive 250.6 units of local currency.
