Scientific Notation, Significant Figures &

Significant DigitsSCH3U

Learning GoalsBy the end of this lesson you should be able to:1. Write numbers, large or small in scientific notation2. distinguish between certain and measured

numbers3. Determine the number of significant digits in a

measurement4. Round to the specified number of significant digits5. Explain the difference between accuracy &

precision6. Determine the correct significant digits based on

lab equipment

Certain NumbersO All counted quantities are exact and

contain an infinite number of significant digits.

O Only whole numbers are possibleO Eg. The number of students in the

class

O Numbers obtained from definitions are exact.O Eg. 1 km has exactly 1000m

MeasurementsO Measurements are not exact.O Are comparisons to a standard O When measuring there is some

level of error or uncertainty

O Eg. What is the length of the clownfish?

AccuracyO Every measurement has a degree of

certainty or uncertaintyO For any measurement, you need to

record all certain digits and one uncertain digit

PrecisionO Is the place value of the last

measurable digitO The more decimal places, the more

precision

O No matter how precise a measurement, it may still not be accurate.

Significant DigitsO Defn: Those numbers that result

from directly measuring an object. It shows the precision of the measurement.

O Units must be included (no units no sd)O The precision of the measurement

depends upon the measuring instrumentO Use the following PRIORITIZED list to

determine the number of sd’s in a measurement, calculation, or conversion

Rule 1: All nonzero digits are significant (they were measured)

OSamplesOa. 234 mOb. 1678 cmOc. 0.23 g

OSD’s and precisionOa. 3 sd to the mOb. 4 sd to the cmOc. 2 sd to the cg

Rule 2: All zeros between nonzero (or significant) digits are significant

OSamplesOa. 202 mmOb. 1003 cmOc. 0.200105 m

OSD’s and precisionOa. 3 sd to the mmOb. 4 sd to the cmOc. 6 sd to the mm

Translation: In between 0s must be measured

Rule 3: Zeros to the right of a nonzero digit but to the left of an understood decimal are NOT significant unless otherwise indicated.

O a. 200 cmO b. 109,000 mO c. 1,000,000 mmO d. 200 cmO e. 200 cm

O a. 1 sd to the mO b. 3 sd to the kmO c. 1 sd to the kmO d. 3 sd to the cmO e. 2 sd to the dm

Translation: 0s at the end of a whole number are NOT measured unless marked.

(a bar over a zero indicates the last measured zero)

Rule 4: All zeros to the right of a decimal point but to the left of a

nonzero digit are NOT significant.

OSamplesOa. 0.0032 mOb. 0.01294 gOc. 0.00000002 L

OSD’s and precision Oa. 2 sd to the .1 mmOb. 4 sd to the .01 mgOc. 1 sd to the .01 mL

Translation: 0s in front of a number less than 1 are NOT measured.

Rule 5: All zeros to the right of a decimal point and following a nonzero digit are significant

OSamplesOa. 20.00 gOb. 0.07080 mmOc. 1.0400 cmOd. 45.00

OSD’s and precisionOa. 4 sd to the cgOb. 4 sd to the .01

mmOc. 5 sd to the mmOd. 0 sd

Translation: 0s at the end of a decimal number are measured.

How to use SD rules when multiplying/dividing

O Rule: Your calculation (answer) must have the same precision as the LEAST precise original measurement

O Find the number of significant digits in each of the starting numbers and note the lowest number of significant digitsO ex. 2.40 cm x 3 cm (lowest # of sd is 1)

O Calculate your answerO Round the answer to the lowest # of sd

found in #1O 2.40 cm x 3 cm = (7.2 cm2) = 7 cm2

Learning CheckMeasurement Significant FIgures

32.07 m

0.0041 g

6400 s

10.0 kJ

100 people (counted)

2. 77.8 km/h x 0.8967 h =

3. 35 000/1.20 L

RoundingO If you are rounding

from a number below 5

O If you are rounding from a number above 5

O If you are rounding from 5

ROUND DOWN

ROUND UP

ROUND TO THE EVEN

Learning CheckO Round to the nearest integer:

1. 1.12. 1.63. 1.54. 2.55. 2.5137

Scientific NotationO Used to express very large numbers

or very small numbers in an easier format

Expression Common Decimal Notation

Scientific Notation

124.5 million kilometres = 124.5 billion meters

124 500 500 km = 124 500 000 000m

1.245 x 108 km =1.245 x 1011 m

154 thousand nanometres

154 000 nm= 0.000154 m

1.54 x 105nm=1.54 x 10-4m

Learning CheckO Write the following values in

scientific notation:a. 35 000b. 0.00000492c. 35d. 1240