Significant Figures 3: Rounding

Rounding to significant figures follows three simple steps. First, count the number of significant figures you want to keep. Second, look at the next digit — we’ll call it the decider. If the decider is five or more, round up. If it’s less than five, the last sig fig stays the same.

Let’s try it. Round forty-seven thousand, eight hundred and thirty-two to three significant figures. Count three sig figs: one, two, three. The decider is three. Three is less than five, so the last sig fig stays the same. Replace the remaining digits with zeros. Forty-seven thousand, eight hundred.

Now a small number. Round zero point zero zero three six seven four to two significant figures. Remember, leading zeros aren’t significant — so start counting from the first non-zero digit. Two sig figs: one, two. The decider is seven. Seven is five or more, so round up — the six becomes a seven. Zero point zero zero three seven.

Round twelve point four eight to three significant figures. Count three sig figs: one, two, three. The decider is eight. Eight is five or more, so round up — the four becomes a five. Twelve point five.

Here’s a tricky one. Round zero point nine nine six to two significant figures. Two sig figs: one, two. The decider is six — that means round up. But nine plus one is ten! So it carries — zero point nine nine six becomes one point zero. We write one point zero — not just one — because we need two significant figures.

So remember the three steps: count your sig figs, check the decider, and round accordingly. Even when rounding causes carries, just follow the process.