What are the rules governing significant figures and rounding?

• Significant figures, or significant digits, establish the value of a number.
• Zeros shown merely to locate a decimal point are NOT significant figures
• Zeros located to the right of another number after a decimal point are significant
• The last significant figure on the right is the one which is somewhat uncertain
• An exact number, such as the number of objects counted, can be considered to have an infinite number of zeros after the decimal point, all of which are significant

• It is impossible to tell how many significant figures are in a large number with zeros to the left of the decimal point without converting the number to scientific notation

• To find the number of significant figures in a given number:

• count all the digits starting at the first non-zero digit on the left

• for a number written in scientific notation count only the digits in the coefficient

• When adding or subtracting numbers, the number of digits to the right of the decimal point in the result should be the same as the number of digits to the right of the decimal point in the number with the fewest digits to the right of the decimal point

• When multiplying or dividing numbers, the number of significant figures in the result is the same as the least number of significant figures in any of the multiplied or divided terms

You will find worked examples at: http://www.ausetute.com.au/sigfig.html