Significant Figures Workshop Outline

The Powerpoint presentation as well as this workshop outline will be available online at the SLC’s wikispace page.

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There are two types of numbers, measured and exact:

Exact numbers have ______.

Measured numbers have ______.

To measure with significant figures, one must measure ______with ______plus ______.

Reading volume correctly requires you to look at the meniscus at ______. For a concave (downward dipping) meniscus like water usually has, we read volume from the ______of the meniscus. For a convex (upward rounded) meniscus, we read volume from the ______of the meniscus.

Meniscus Practice

A) ______B)______

Let’s Measure!

There are 9 stations set up with different measuring devices and things to be measured. Using the principles of measuring that we have just gone over, make each measurement to the correct number of sig figs. J

1) / 2) / 3)
4) / 5) / 6)
7) / 8) / 9)

Identifying Significant Figures in Numbers that We Are Given

Non-zero numbers in a given measured value are ______significant.

The Rules of Zero

1) Leading zeroes (zeroes before non-zero numbers) are ______significant. EXAMPLE: 0.00000259 m

2) Sandwiched zeroes (zeroes between non-zero numbers) are ______significant. EXAMPLE: 10029 J

3) Trailing zeroes (zeroes after non-zero numbers) are ______significant ____ the value has a decimal point.

EXAMPLE: 12500 lbs (NOT significant) 12.500 lbs (significant)

How many significant figures are in each of the following measured numbers?
A) 45.8736 ______
B) .000239 ______
C) .00023900 ______
D) 48000. ______
E) 48000 ______
F) 3.982´106 ______
G) 1.00040 ______/ Rounding to the correct number of significant figures.
Round each of the following values to 3 significant figures.
A) 1.5587 ______
B) .0037421 ______
C) 1367 ______
D) 128,522 ______
E) 1.6683 ´106 ______

Adding and Subtracting with Significant Figures

Rule: The sum or difference of two or more measured values must have the same precision (uncertainty) as the least precise measurement (greatest uncertainty).

What this means: 124.56 (The uncertainty is in the hundredths place)

+ 4.5 (The uncertainty is in the tenths place.)

129.1 (Answer has uncertainty in the tenths place.)

Notes:

Practice Adding and Subtracting with Significant Figures

Calculation / Your Calculator’s Answer / Answer with Correct Sig Figs
A) .56 + .153 =
B) 82000 + 5.32 =
C) 10.0 - 9.8742 =
D) 10 – 9.8742 = / .713 / ______
82005.32 / ______
.12580 / ______
.12580 / ______

Multiplying and Dividing with Significant Figures

Rule: The product or quotient of two or more measured values must have the same number of significant figures as the measured value with the fewest significant figures.

Example: 3.210 m×6.5 m=21

4 S.F. 2 S.F. 2 S.F.

Notes:

Practice Multiplying and Dividing with Significant Figures

Calculation / Your Calculator’s Answer / Answer with Correct Sig Figs
A) 32.27 ´ 1.54 =
B) 3.68 ¸ 0.07925 =
C) 1.750 ´ 0.0342000 =
D) 3.2650´106 ´ 4.858 =
E) 6.022´1023 ´ 1.661´10-24 = / 49.6958 / ______
46.4353312 / ______
0.05985 / ______
1.586137 ´ 107 / ______
1 / ______