We want to subtract the two given numbers.
0.03-0.04
Notice that both numbers are repeating decimals. To subtract them, we can rewrite both numbers as fractions, or we can leave them in this form. We will get the same answer either way. Let's use the fraction method. Recall how to rewrite 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 our decimals as fractions, starting with the one on the left. We will substitute 0.03 for d and 2 for n, as there are two repeating digits in the decimal.
ccc x=d & ⇔ & x= 0.03 10^nx=10^n d & ⇔ & 10^2x=10^2( 0.03)
Let's simplify the second equation.
10^1x=10^2(0.03) ⇒ 100x=3.03
Now we are ready to subtract the first equation from the second one.
c r c l& 100x & = & 3.03 -( & x & = & 0.03 ) & 99x & = & 3
Next, we can solve for x. Let's do it!
The first number can be written as 399. Now let's find the fraction form of the second given number.
c r c l& 100x & = & 4.04 -( & x & = & 0.04 ) & 99x & = & 4
Let's solve for x.
