Evaluate 1 - (0.3/1.54).

Step-by-step solution

1. 1

   Do the division before the subtraction. Parentheses and the standard order of operations both put $\tfrac{0.3}{1.54}$ first; only then is it subtracted from $1$.

2. 2

   Clear the decimals from the quotient. Multiplying numerator and denominator by $100$ leaves the value unchanged: $\frac{0.3}{1.54} = \frac{30}{154}.$ Working with integers from here on removes any rounding risk.

3. 3

   Reduce the fraction. Both $30$ and $154$ are even, so divide by $2$: $\frac{30}{154} = \frac{15}{77}.$ Since $77 = 7 \cdot 11$ shares no factor with $15 = 3\cdot5$, this is in lowest terms.

4. 4

   Subtract from 1 using a common denominator. Write $1 = \tfrac{77}{77}$: $1-\frac{15}{77} = \frac{77-15}{77} = \frac{62}{77}.$

5. 5

   Convert to a decimal only at the end. $\dfrac{62}{77} = 0.8051948051948\ldots$, a repeating decimal with period $0519480$, so $\approx 0.80519$. Reporting $\tfrac{62}{77}$ is exact; the decimal never terminates.

6. 6

   Interpret the result. If $0.3$ out of $1.54$ is removed, the fraction remaining is $\tfrac{62}{77}\approx 80.5\%$ - the complement form $1-\tfrac{a}{b} = \tfrac{b-a}{b}$ is worth remembering as a one-step shortcut.