Step 1: Understand why sand grain size needs a single number.
Moulding sand is never made of perfectly uniform grains, it is a mixture of many grain sizes, so foundries need one standardised number that summarises this whole distribution for quality control and comparison purposes.
Step 2: Recall how that number is actually obtained.
A weighed sample of dried sand is passed down through a stack of standard sieves with progressively finer mesh openings, and the amount of sand retained on each sieve is recorded as a percentage of the total.
Step 3: Combine those results into the standard index.
Each sieve is assigned a fixed multiplier, and a weighted average is calculated from the percentage retained on every sieve, producing a single figure known as the Grain Fineness Number, or GFN. A high GFN points to fine grained sand while a low GFN points to coarse grained sand, and this is the standard, universally used way of expressing moulding sand grain size in the foundry industry.
\[ \boxed{\text{grain fineness number}} \]