SCIENTIFIC NOTATION & SIGNIFICANT FIGURES

Scientific Notation Multiple of Power of 10 Exponents Decimals placed after the first digit Can be used for any size number zillions to picons

Examples of Scientific notation 1 000 g = 1.0 x 10 3 g 0.04 mL = 4.0 x 10 -2 mL

Why use scientific notation? Less chance of clerical mistake (0000?) very large & very small numbers No zeros as placeholders

Why use scientific notation? Leaves no doubt the zeros are part of an accurate measurement Confirms the reliability of the instrument ( dm? cm ? mm? )

Multiplying and Dividing in Scientific Notation Exponents represent the “powers of ten” Same base number of “10” WORK with exponents only

Multiply (x) ADD (+) EXPONENTS

1000 x 100 = 100 000 10 3 x 10 2 = 10 3 + 2 = 10 5

When you Multiply (X) in Scientific Notation ADD EXPONENTS 10 3 + 2 = 10 5

Example (3 x 10 5 ) x ( 2 x 10 4) = ?

1) Multiply coefficients (3 x 2) = 6 2) Add exponents 10 5 + 4 = 10 9

Final Answer (3 x 10 5 ) x ( 2 x 10 4) = 6 x 10 5 + 4 = 6 x 10 9

Sometimes the calculated answer is not in correct Scientific Notation: Use Scientific Notation rules to fix ( 5 x 10 2 ) x ( 7 x 10 4 ) = 35 x 10 6 35 = (3.5 x 10 1) x 10 6 = 3.5 x 10 7

SUBTRACT (-) EXPONENTS Divisor - numerator DIVISION SUBTRACT (-) EXPONENTS Divisor - numerator

Operate on the coefficients; Then subtract exponents 6 x 10 7 = Problem: 2 x 10 5 6 x 10 7 = 2 10 5 Operate on the coefficients; Then subtract exponents

Subtract Exponents 6 x 10 7 – 5 2 = 3 x 10 2

Sometimes the answer is not in correct Scientific Notation Use Scientific Notation rules to fix 4 x 10 5 = 0.5 x 10 3 = 8 x 10 2

Problem: 0.5 x 10 3 = Change to Sci Notation first, then finish (5.0 x 10 –1) x 10 3 = 5.0 x 10 –1 + 3 = 5.0 x 10 –1 + 3 = 5.0 x 10 2

Final Answer Correct scientific notation Measurement units Correct number of significant figures

What is a significant figure (digit)? Significant Figures What is a significant figure (digit)?

Significant Figures 1. Any non-zero number 2. Zero between non-zero numbers 3. Zero after a decimal & a non-zero 4. Zero that has been physically counted

Significant Figures Not significant!!! 5. Zero as a place holder 1. Any non-zero number 2. Zero between non-zero numbers 3. Zero after a decimal & a non-zero 4. Zero that has been physically counted Not significant!!! 5. Zero as a place holder 0.001 or 1 000

How many significant figures? 0.05319 ______ 70 495 ______ 687 ______ 0.07080 ______ 0.000873 ______ 112 000 ______ 400.00 ______ 0.0200 ______

Practice rounding to the correct number! What happens when your answer is not the right number of significant figures? Practice rounding to the correct number!

Rounding to the right Sig Fig # 0.053 19 ________________ (2) 70 495 ________________ (3) 687 ________________ (1)

Add or Subtract Line up vertically (up-down) Line up decimal places Round to the lowest column that each has a measured number NEVER fill in zeros when they were not measured Remember units in answer

Find the sum to the correct sig fig 27. 8 6 5 g 4. 2 g + 3. 0 5 g 35. 1 15 g

Find the sum to the correct sig fig 27. 8 6 5 g 4. 2 g + 3. 0 5 g 35. 1 15 g

Add or Subtract 3 5. 1 1 5 g lowest common column is the tenths’ place Round to 35.1 g

Practice! What is the perimeter of this figure? 1.2 cm + 1.2 cm + 4.56 cm + 6.798 cm

Practice! What is the perimeter of this figure? 1.2 cm 1.2 cm 13.758 ~ cm 4.56 cm 6.798 cm 13.758 cm

Remember do not add zeros in! What is the perimeter of this figure? 1.200 cm 1.200 cm 13.758 ~ cm 4.560 cm 6.798 cm 13.758 cm

Multiply or Divide Count the number of Significant Figures in each measurement for the problem Answer can only have the number of significant figures based on the lowest # of sig figs part (measurement)

Multiply or Divide Example 7.6 cm x 12.35 cm = __ SF __ SF Final answer can only have __ SF

Multiply or Divide Example Final answer = 93.86 cm 2 can only have __ SF so ~ 94 cm 2

Multiply or Divide Example __ SF __ SF Final answer can only have __ SF

Example Final Answer in Sig Fig 27.86 5 m x 4.2 m = 117.033 m2 Round to 2 SF = 120 m2 Remember keep value of the number! 117.033 ~ is about one hundred & twenty Not 12! Think $$$$$

How do I know how many significant figures in my answer? When Adding or Subtracting: Adjust/Round to the lowest common column or lowest common decimal place When multiplying/dividing Adjust/round to the lowest number (count each element) of sig figs in the problem

Practice

Practice

Practice