Sig+Fig

=Significant Figures and Rounding= The number of figures or digits used to write the value of a measured or calculated quantity shows how precisely the value is known.

For example, 4.2 cm means that I measured something and I compared it with the tenth of a centimeter (millimeter) markings. This has two significant figures: centimeters and tenths of centimeters. I didn't look any closer at the ruler, and I don't know anything about possible fractions of a millimeter. The "real" value could be anywhere from 4.15 cm to 4.24 cm. I don't know anything about the hundredths of a centimeter. Another example: A playground is 24 m wide. I used a meter stick to measure it and kept marking the end of the meter stick with my foot before moving it along. I know I counted 24 meters, but because of the rough method I used for the measurement, I'm not sure about fractions of a meter. This value has two significan figures. The "real" measurement could be anywhere from 23.5 to 24.4 m

Significant figures are the figures that are used to show the precision of the measurement. Sometimes zero is a significant figure because zero IS one of the possible markings on the measuring instrument that is used.

For example, a measurement of 4.0 cm has two significant figures and means that I measured something, I looked at the tenth of a centimeter markings (millimeters) and saw that it was closest to the zero millimeter mark (right on the centimeter mark). That is different from a measurement of 4 cm that means I measured something and only looked at the centimeter markings. 4 cm means I'm not sure if there were a few millimeters more or less. BE CAREFUL! Your calculator doesn't know the difference between 4.0 and 4. When doing calculations YOU have to do the work of figuring out how precisely you know the answer.

Sometimes zeros are used a place holders to make sure the other figures are the right size. Place holder zeros are NOT significant and do NOT show anything about the precision of the value.

Looking back at the first example: 4.2 cm is the same amount as 0.042 m. Converting to a different unit does nothing to the precision and does not change the number of significant figures - it's still two sig fig. The zeros are just placeholders. We could also write this measurement as 0.000042 km and it would still only have 2 sig fig. Similarly, the measurement of 24 m is the same amount as 2400 cm and 0.024 km. All of these numbers have 2 sig fig.

Unfortunately, most people get rather careless with zeros as significant figures when they are to the left of the decimal point. 2400 cm might mean 2, 3 or 4 significant figures, depending on whether you actually looked at the meter markings the 10 cm markings and the cm markings on the measuring tool. Strictly speaking, zeros to the left of an unwritten decimal point and to the right of other figures are NOT significant. 100 m, 30 s, 5000 km all have 1 sig fig. However, you will often encounter numbers that are written with zeros so that they only show one sig fig, but your general knowledge of the measuring method or tool would give you good reason to assume more precision. A car is traveling at 80 km/h (you should know that car speedometers measure to within 1 km/h so this is probably precise to two sig fig.) The temperature is 30 degrees today (thermometers are usually precise to 1 degree, so this is probably two sig fig.)

To be most careful about significant figures, scientists make use of scientific notation. This is a way of writing numbers with the decimal point ALWAYS after the first non-zero figure, and then multiplying the number by a power of ten to make the value the right size. Any zeros after the decimal point are put there especially to show the level of precision and ARE SIGNIFICANT.

2400 cm = 2.4x10^3 cm has 2 sig fig; 2.40x10^3 cm has 3 sig fig; 2.400x10^3 cm has 4 sig fig

To summarize the rules about significant figures: all examples with 4 significant figures
 * bold **

, non-significant figures // italic //

. // 0.00 //** 2390 ** **7,808**,//000//
 * 1) All non-zero figures are significant.
 * 58.21 **
 * 1) All zeros between non-zero figures are significant.
 * 2004**
 * 1) All zeros to the right of BOTH the decimal point AND a non-zero figure are significant.
 * 5.600 **
 * 1) Zeros to the right of the decimal point are significant if they are not followed by a non-zero figure.
 * 34.00 **
 * 1) Zeros to the left of non-zero figures are not significant.
 * 1) Zeros to the right of non-zero figures are usually not significant if no decimal point is shown.

When you are calculating using measurements, generally the precision of your answer will depend on the precision of the original measurements.