Significant Figures, Rounding and Truncating

Significant Figures The significant figures (digits) in a measurement include all the digits that can be known precisely plus a last digit that is an estimate.

The rules for determining which digits in a measurement are significant are: Every nonzero digit in a recorded measurement is significant m, m and 714 m all have three significant figures. Zeroes appearing between nonzero digits are significant. The measurements 7003 m, m, and m all have four significant figures. Zeroes in front of (before) all nonzero digits are merely placeholders; they are not significant only has two significant figures.

The rules for determining which digits in a measurement are significant are: Zeroes at the end of the number if a decimal point is present and also zeroes to the right of the decimal are significant. The measurements m, m and all have six significant digits. Zeroes at the end of a measurement and to the left of an omitted decimal point are ambiguous. They are not significant if they are only place holders: 6,000,000 live in New York—the zeroes are just to represent the magnitude of how many people are in N.Y. But the zeroes can be significant if they are the result of precise measurements. A vinculum over the least significant zero is often used.

The significant figures in a number in scientific notation is the number of digits in the mantissa. The number 4×10 5 has only one digit in the mantissa, so it has one significant figure ×10 5 has 4 significant figures. Thus the number 1200 which is unclear as to how many significant figures it has is more clearly expressed as 1.200×10 3 as having 4 significant figures or as 1.2×10 3 as having 2.

When calculating with significant figures, an answer cannot be more precise than the least precise measurement.

This means for... Addition and subtraction: the answer can have no more digits to the right of the decimal point than are contained in the measurement with the least number of digits to the right of the decimal point. For example: m m m = m, but the answer must be rounded to m, or 3.425×10 2 m. Specification of units is also extremely important. Multiplication and division: the answer must contain no more significant figures than the measurement with the least number of significant figures (the position of the decimal is irrelevant).

It is very important to round rather than truncate your results: not You are often instructed to round to so many significant digits or to such and such a level of precision. There are variations, but the standard rule would round anything from $0.50 up to $1.49 all to $1.