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Physics 11 - Chapter 1 & 2 What is physics and Mathematical tools

Lesson #2 Significant Figures

Physics involves collecting data. This involves measuring, and every measuring apparatus has a

limit to how precise we can make a measurement. Because of this, the digits in our calculations

that we know with certainty are also limited.

Given a measurement, not all numbers are “significant” (should be taken as accurate). When

using several measurements to calculate something, it’s important to know what’s important in the

end.

RULES FOR ‘SIG FIGS’

1. Any non-zero number counts

456 3 sig figs

0.9723 4 sig figs

2. Zeros to the left of a decimal count.

690. 3 sig figs

690 2 sig figs no decimal

3. Zeros to the right of a decimal are tricky. If there are numbers to the left of a zero, they count,

otherwise ignore them…

67.00 4 sig figs

67.0001 6 sig figs

0.00035 2 sig figs

0.00305 3 sig figs

0.008900 4 sig figs

Significant Digits (sig figs): The valid digits in a measurement.

7 → 1 sig fig

5.2 → 2 sig figs

0.2 → 1 sig fig

0.23 → 2 sig figs

0.008 → 1 sig fig

0.0080 → 2 sig figs

186,000 → ???

(As is, there are 3. But scientific notation will tell us.)

1.86×105 → 3 sig figs

1.86000×105

→ 6 sig figs

1.860×105 → 4 sig figs

1. Non-zeros are always significant.

E.g. 344 → 3 sig figs

2. All final zeros after the decimal point are significant.

E.g. 3.440000 → 7 sig figs

3. Zeros between two sig figs are significant.

E.g. 3.102 → 4 sig figs

4. Zeros as placeholders are NOT.

E.g. 0.0002 → 1 sig fig

Rules for + and - : How to add (subtract)

The answer must have the same number of digits after the decimal as the measurement with the least

number of digits after the decimal point.

Use the least accurate measurement (by decimal place) in your final answer.

E.g. mmmm 53928.158372.12783.634.7

mm 54.153928.1

Since 7.34m is the least accurate measurement, with two decimal places.

Rules for and : How to multiply (divide)

The answer must have the same number of significant figures as the measurement with the least number

of significant figures.

Use the measurement with the fewest sig figs in your final answer.

E.g. kmkm 774.44min1.6min34.7

kmkm 45774.44

Since 6.1min has the fewest sig figs (two).

Any digit (1 - 9) is a significant digit. ex:

Zeros may or may not be significant.

Zeros at the beginning of a quantity are not significant. ex:

Zeros that are between significant digits are significant. ex:

Zeros at the end of a quantity may or may not be significant. ex:

1. How many significant figures are in the following numbers?

a) 425 b) 1.2

c) 25.2 d) 6.3706

e) 8.11002 f) 2500

g) 450,000 h) 5080.

i) 0.00897 j) 0.1000

k) 7.01 x 103 l) 7.00 x 10

-4

m) 0.0089700

2. Compute the following - use significant figures.

a) 6.3 + 10.764 + 4.56 b) 67.98 + 8 + 43.2

Where do you round off?

RULE #1 Never round off until ALL your calculations are finished.

RULE #2 Round off to the smallest number of significant digits represented.

c) 56 x 3.21 d) 3.72 2.1

RULE #1 Use all known digits in the calculation.

RULE #2 Round off to the last decimal place that both numbers have in common.

Unit Conversion:

Ex. 1) Convert the following distances to meters:

a) 1.1 cm b) 76.2 pm c) 0.123 Mm

Scientific Notation:

Rewrite the following in scientific notation:

Ex. 1) The Earth weighs 5,980,000,000,000,000,000,000,000 kg.

Ex. 2) One electron has a charge of 0.00000000000000000016 Coulombs.

Ex. 3) 3 5

8 1

(1.8 10 )(2.6 10 )

(9 10 )(1.3 10 )

What is the difference between $600 and $599.87 ?

(besides 13 cents)

One is more precise than the other. Scientifically, we say that one has more significant (relevant) digits

than the other.

$600 has

$599.87 has

Assignments: page 18 #6 page 24 #12, 13 page 25 # 15 page 26 #16, 17