Fractions, Decimals and Order-of-Magnitude Estimation
This domain is about speed and sanity-checking. Many EPSO items cannot comfortably be solved exactly in the time available, and are designed so that a two-significant-figure estimate picks the right option out of four plausible ones.
Benchmarks worth memorising
- 1/8 = 0.125; 3/8 = 0.375; 5/8 = 0.625; 7/8 = 0.875
- 1/6 ≈ 0.1667; 1/3 ≈ 0.3333; 2/3 ≈ 0.6667
- 1/7 ≈ 0.1429; 1/9 ≈ 0.1111; 1/11 ≈ 0.0909
- 1/16 = 0.0625; 1/12 ≈ 0.0833
- Percentage equivalents: 1/8 = 12.5%, 1/6 ≈ 16.7%, 1/5 = 20%, 1/4 = 25%, 1/3 ≈ 33.3%
Comparing fractions
Cross-multiply: to compare 7/12 with 11/19, test 7 × 19 = 133 against 11 × 12 = 132. The first fraction is larger. This is faster and safer than converting both to decimals.
Estimation discipline
Round to one or two significant figures, compute, then track whether the rounding pushed the answer up or down. If every factor was rounded up, the true value is below your estimate - use that to choose between adjacent options. Never round one factor up and another down and then try to reason about the net error.
Worked example
A budget of €4,987 is spent at 19.8% on training. Which option is closest: €790, €990 or €1,190?
Estimate: 5,000 × 0.20 = 1,000. Both factors were rounded up, so the true value is slightly below 1,000. Only €990 fits. Exact: €987.40.
Cancelling before multiplying
In a chain of multiplications and divisions, cancel common factors across the whole expression first: (48 × 35)/(14 × 12) reduces to (4 × 5)/2 = 10, avoiding large intermediate numbers.
Traps
- Rounding numerator and denominator in the same direction, which can shift a ratio substantially.
- Cancelling across an addition sign, which is not a valid operation.
- Assuming a larger denominator always means a smaller fraction, without checking the numerator.
- Selecting the option that reproduces an intermediate rounding artefact.