Rounding to Significant Figures
Pick the tab marked Round, enter a number and how many figures to keep. The method is below the tool.
Counted digits: 450
- →Every non-zero digit is significant.
- →Leading zeros only place the decimal point, so they are not significant.
- →Trailing zeros after a decimal point record precision, so they are significant.
The method
- 1. Find the first significant digit. The first non-zero digit, reading left to right. In 0.004567 that is the 4.
- 2. Count forward to the last digit you keep. For 3 significant figures in 0.004567, that is the 6.
- 3. Look at the next digit only. 5 or more rounds up, 4 or less leaves it. The digits beyond it do not get a vote.
- 4. Replace the rest with nothing, or with zeros. After a decimal point they vanish; before it they must stay as placeholders — which is how rounding can create an ambiguous number.
Where rounding creates ambiguity
Round 12,345 to three significant figures and you get 12,300. But 12,300 written plainly reads as three, four or five figures depending on who is reading it. The only way to say three and be understood is 1.23 × 10⁴. The calculator flags this whenever it happens rather than handing back a number that quietly misstates its own precision.
Why not just use a spreadsheet
Because floating-point arithmetic rounds the wrong way at exactly the boundary that matters. 1.005 to three significant figures is 1.01, but the nearest double to 1.005 is slightly below it, so the usual multiply-round-divide trick returns 1.00. This calculator rounds the digits as written, so the boundary cases come out right.