Significant Figures 1: Bob's Bank Account

Meet Bob. Bob says he has three million dollars in his bank account.

When someone says three million, do they mean exactly three million? Not a dollar more, not a dollar less? Probably not. Bob’s real balance could be anything — maybe three million, two hundred and forty seven thousand. He’s just rounded to the nearest million.

So the three is the only digit we can trust. It’s the digit Bob is giving us with confidence. The rest of the digits? They’re probably just the result of rounding. Bob’s real number could have anything in those columns, but he’s rounded them away. That means only one digit is significant.

But what if Bob says three million and one? That changes everything. That one dollar at the end tells us he hasn’t rounded at all. It wouldn’t make sense to say three million and one if the other digits were just rough estimates. Every digit is exact. All seven digits are significant.

And if Bob says three million dollars and zero cents? That decimal point is a deliberate choice. He’s telling us the amount hasn’t been rounded at all — it’s accurate to the nearest cent. Every digit counts. That’s nine significant figures.

Let’s recap. The way a number is written tells us whether it’s been rounded. Trailing zeros without a decimal point? The number has probably been rounded — those zeros aren’t giving us real information. But a non-zero digit at the end, or a decimal point? That tells us the number is precise — every digit is significant.