# what are the significant figures ?

what are the significant figures for

6.022 x 10to the power 23

1.79 x 10 to the power -19

3.00 x 10 to the power 8

Relevance

Significant figures:

“The uncertainty in a measurement is an estimate of how

much larger or smaller another measurement of the same

quantity is likely to be”.

3.2  0.1 cm , or 3.24  0.01 cm.

The digits that are obtained as a result of measurements

are called significant figures.

Zeros that lie to the left of the first non-zero digit are not

significant figures. “A zero that lies to the right of a decimal

point and also to the right of the first non-zero digit always

counts as a significant figure”.

0.0054070 has 5 significant figures.

For multiplication or division, the product or quotient

should not contain more significant figures than are

present in the least precise factor in the calculation.

Area = 6.2 cm x 7.01 cm = 43 cm2 and not 43.5 cm2, i.e. 2 significant figures only.

-Precision and accuracy:

“Precision refers to how closely measurements of the same quantity

come to each other” i.e. How a measurement is uncertain  0.1 or 

0.01,----------- etc.

*Accuracy refers to how close an experimental observation lies to the

true value”.

** A more precise measurement is a more accurate one.

- The amount of uncertainty in a sum or difference will be at least as large as the largest uncertainty in any of the terms involved in the calculation.

4.37153 + 302.5 = 306.9, and not 306.87153, i.e. four significant figures only.

For addition and subtraction, we round the answer so it has the same number of decimals as the quantity with the fewest number of decimals.

- Exact numbers:

Those are coming from the definition or direct counting e.g. 3 ft = 1 yd or 4.25 yd x (3 ft/yd) = 12.8 ft.

The number of significant figures is determined solely by the number of

significant figures of the measured length and not the labelled factor(3).