Significant Figure Rules

Rules Examples

The following are always significant•Non zero digits•Zeros between non zero digits•Zero to the right of a non zero digit and to the left of a written decimal•Finishing zeros to the right of a decimal place

673 has 3

506 has 3

1.009 has 4

57.00 has 4

The following are NEVER significant•Zeros to the left of the first non zero digit

0.67 has 20.004 has 1

EXCEPTIONS•Counting numbers•Exact conversion factors

30 days in June100 cm in 1 m

Math in Significant Figures

• Multiplication and Division– The # of significant figures in the

result is the same as the # in the least precise measurement used in the calculation

– 0.024 x 1244= (two significant figures )

• Sample Problem: Find the area of a rectangle 2.1 cm by 3.24 cm.– Solution: Area = 2.1 cm x 3.24 cm = 6.8cm2

Math in Significant Figures

• Addition and Subtraction– The # of significant figures in the result has the same

number of decimal places as the least precise measurement

– Round to the least # of decimal places• Sample Problem: Add 42.56 g + 39.460 g + 4.1g

Solution:42.56 g

39.460 g4.1 g

Sum = 86.1 g

Rules for Rounding

• In a series of calculations, carry the extra digits through to the final result, then round

• If the digit to be removed– Is less than 5, the preceding digit

stays the same– Is equal to or greater than 5, the

preceding digit is increased by 1

Scientific Notation

Why use Scientific Notation?

M x 10n

• M is a number between 1 and 10• n is an integer• all digits in M are significant

– if n = (+)#, then move the decimal to the right

• 1.0 x 105 = 100000

– If n = (-)#, then move the decimal to the left

• 1.0 x 10-5 = .00005

Sample Problems

• Express these numbers in decimal notation.

1. 8.32 x 10-2 _____________

2. 5.4 x 104 ______________

3. 9.67 x 103 _____________

4. 1.457 x 102_____________

5. 3.00 x 10-1 _____________

6. 2.22 x 10-6 _____________

Reducing to Scientific Notation

1. Move decimal so that M is between 1 and 10

2. Determine n by counting the number of places the decimal point was moved

a. Moved to the left, n is positive

b. Moved to the right, n is negative

Sample Problems

• 47,000 _____________________

• 0.00047 ____________________

• 0.4100 _____________________

• 421 _______________________

• 5630 _______________________

Mathematical Problems

• Addition and subtraction– Operations can only be performed if the

exponent on each number is the same

• Multiplication– M factors are multiplied– Exponents are added

• Division– M factors are divided– Exponents are subtracted (numerator -

denominator)

Sample Problems

1. (2.8 x 10 5) +(7.53 x 10 5)________________________

2. (3.1 x 10 -2) (4.380 x 10 3)________________________

3. (4.20 x 10 2) (0.040 x 10 -1)________________________

4. 3.0 x 10 3 ÷ 1.2 x 10 4 ________________________

5. 4.95 x 10 6 ÷ 2.33 x 10 -2 ________________________