# Accuracy and Precision

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Physical measurements necessarily yield approximations. Although we can measure some lengths with astonishing accuracy, we can't measure any perfectly. Some inexactness, if only one part in thousands, remains. If we try to get too fine with determining length, say of an iron rod, our object-level notion of rigid boundaries fails. We reach a level of atomic structure where the "iron rod" is in flux without exact boundaries.

Precision
Refers to the number of significant digits and/or decimal places that can be reliably determined with a given instrument or technique.
Accuracy
Refers to how close a measured value is to the "true" or correct value.
Significant figures
Those figures in a measurement that are known with reasonable accuracy.

The following rules apply to determine how many significant figures a measurement has:

• All digits other than zero are significant.
• Zeros between non-zero digits are significant.
• Leading zeros in a number are not significant.
• Trailing zeros in a number may or may not be significant. Use standard form when appropriate to avoid confusion.

Here are some examples of significant figures:
 327 three significant digits 2.09 three significant digits 0.000000382 three significant digits 16.83 four significant digits 3.2 two significant digits 3.20 three significant digits 150,000,000 not clear how many significant digits. Use scientific notation to clarify. 1.5 × 108 two significant digits 1.50 × 108 three significant digits

## When rounding off measurements:

• When the digit immediately to the right of the last digit to be rounded is less than five, the last digit is unchanged.
• When the digit immediately to the right of the last digit to be retained is greater than five (or is equal to five, with non-zero digits following), the last digit retained is increased by one.
• When there is only one digit to the right of the last digit to be retained, and it is 5, the last digit to be retained remains unchanged if even and is increased by one if odd.