# Significant Figures and Resolution

Significant figures are often forgotten when we use the data in the
database.

By the rule of the database, there is the case that many figures are used even if significant figure is one.

##
Significant Figures

The significant figures are two for "**3.0**."
The significant figure is one for "**3**."
The number of figures tells us the significant figures.

Because of the rule the data in the database may not tell us the significant figures.
We need to compare some data or study the ability of the measurement.

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Significant Figures Tells Us the Significant Area of Calculation

**3.0 + 2.0** : The answer is "5.0". Significant figures are two.

**3 + 2** : The answer is "5". Significant figure is one.

**3.0 + 2** : The answer is "5". Significant figure is one.

The smallest figure is the significant figure of calculation for addition, multiplication and division.

##
Difficulty of the Combination of Large Number and Small Number

**3.0 + 0.0012** : The answer is "3.0". Significant figures are two.
The small number does not affect the calculation.

If we want to use the number, we need to change from "3.0" to "3.0000.

"
**3.0000 + 0.0012** : The answer is "3.0012". Significant figures are five.

##
Difficulty of Subtraction

**2.23 + 2.21** : The anser is "0.02". Significant figure is **one**.

Subtractions often reduce the significant figures.

For example, we need to care about the calculation of
standard deviation
and
normalization.

We can prevent the reducing by changing the order of the calculation.

Errors by Significant Figures

NEXT Errors by Significant Figures