Apply the examples with Rounding Calculator. Check the worked steps below, then practice on your own.
Two different ways to describe precision
Decimal places answer “how many positions are shown after the point?” For 12.345, that is three. Significant figures answer “how many digits express the measured or reported value?” For 12.345, there are five.
These ideas overlap but are not interchangeable: small numbers with leading decimal zeros illustrate the difference clearly.
Examples side by side
| Number | Decimal places | Significant figures |
|---|---|---|
| 3.14 | 2 | 3 |
| 0.00450 | 5 | 3 |
| 12.005 | 3 | 5 |
| 0.050 | 3 | 2 |
| 7.000 | 3 | 4 |
Leading zeros before the first nonzero digit are not significant. Zeros between significant digits, and trailing zeros shown after a decimal point, are significant.
Leading and trailing zero rules
In 0.00072, the zeros before 7 position the decimal number but do not increase the significant-figure count. The significant digits are only 7 and 2, so there are two.
In 0.7200, the zeros after 72 are significant because they are displayed to the right of the decimal point; there are four significant figures.
Rounding to decimal places versus significant figures
0.004963 to three decimal places becomes 0.005. To three significant figures it becomes 0.00496. The first rule fixes position after the decimal; the second retains the first three meaningful digits.
For 1234.56, rounding to two decimal places leaves 1234.56 unchanged, while rounding to two significant figures gives about 1.2 × 10³.
Why scientific notation helps
Scientific notation can make the count of significant figures explicit. Compare 1.20 × 10³ (three significant figures) and 1.2 × 10³ (two significant figures). Both represent approximately 1,200, but the written precision differs.
A number written simply as 1200 can be ambiguous about trailing-zero significance; scientific notation communicates the intent more clearly.
Real-world calculator reporting
For currencies, two decimal places are common. For laboratory measurements, significant figures may better reflect the resolution of instruments. The choice should follow the context, not the number of digits a calculator is capable of showing.
- 0.0600 has 4 decimal places and 3 significant figures.
- 54.20 has 2 decimal places and 4 significant figures.
- 4.056 has 3 decimal places and 4 significant figures.
Frequently asked questions
How many significant figures are in 0.00450?
Three: the digits 4, 5 and the final displayed 0.
Is 1000 always four significant figures?
Not necessarily. Without a decimal marker or scientific notation, trailing zeros in an integer can be ambiguous.
Why does 1.20 contain three significant figures?
The last zero is to the right of the decimal point and indicates reported precision.
Open the Rounding Calculator, then explore Scientific Notation Calculator for more practice.