SIGNIFICANT FIGURES AND ERROR

Determining Significant Figures (Significant Digits) 1. Every non-zero digit is significant. Thus, 21.8, 0.283 and 567 all have three significant digits.

2. Zeros appearing between non-zero digits are significant. Thus, 505 and 0.206 have three significant digits, while 50,005 has five significant digits.

3. Zeros appearing in front of significant digits are not significant. They are merely place-holders. Thus, 0.000456 and 0.203 both have three significant digits.

4. Zeros at the end of a and to the right of the are significant. Thus 3.000 has four significant digits and 3000.0 has five significant digits.

5. Zeros at the end of a number and to the left of the decimal are tricky. Normally they are not significant. Thus, the distance from the Earth to the Sun, 93,000,000 miles is two significant digits. The speed of light, 186,000 miles per second, has three significant digits. However, if you know from other information that some of the ending zeros were actually measured, they can be significant. Assume trailing zeros are not significant unless you are told otherwise. If you need to indicate that zeros after a number are significant, use , DO NOT simply put a decimal point at the end of a number!! For example 1.00 x 102 has three significant figures. Writing 100. Is ambiguous, and it will be marked incorrect.

6. Finally, counted or defined have an infinite number of significant digits. If there are five people in your family, this is an exact number. There are exactly 3 feet in a yard.

Calculating with Significant Figures (Significant Digits) 1. The result of a multiplication or division has the name number of significant figures as the least precisely known quantity in the calculation. Thus 3.14159 2.0 = 6.3

2. The result of an addition or subtraction should be expressed with the same 32.7 number of decimal places as the quantity carrying the smallest number of +0.15779 32.9 decimal places. Thus 2 C, converts to 275 K, which has 3 significant figures.

3. The number of significant figures in a quantity is equal to the number of digits after the decimal in its . Thus the log of 3.51  10–7 is –6.455, and 102.65 is 4.5 x 102.

Rounding Error When you do a long series of calculations, try to do them all in one set of operations. If you must write down intermediate steps, don't round them. If you do, your answer will be no more accurate than the least accurate of the intermediate calculations. For example, how many miles are in 36.70 centimeters? (Note that there are exactly 2.54 cm in an inch and exactly 12 inches in a foot.)

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or by doing it in steps:

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