Significant Figures 2: Leading Zeros

Bob is measuring a tiny seed. He says it’s 5 millimetres wide. That’s one significant figure — just the five.

But what happens if we write the same measurement in metres? Five millimetres is zero point zero zero five metres. It’s the same seed. The same measurement. The same ruler. Nothing about the precision has changed. So when we look at it this way, 0.005m and 5mm should have the same number of significant figures. They both have 1 significant figure, the 5. Leading zeros don’t count as significant.

Let’s try another. Twenty-five millimetres — that’s two significant figures, the two and the five. In metres, that’s nought point nought two five. Same measurement, still two significant figures. The leading zeros don’t count.

This makes sense from the other direction too. Remember Bob’s three hundred and fifty thousand dollars? We said that’s two significant figures — the three and the five. But think about it. There are zeros in the millions column too. And the ten millions. And the hundred millions. Those are all leading zeros — columns that Bob’s number doesn’t even reach. Nobody would count those as significant. Leading zeros never count — whether they’re written down or not.

So here’s the rule. Leading zeros are never significant. They’re just placeholders. Always start counting significant figures from the first non-zero digit.