Chem 11 Lesson 1.2

Measurement – Precision

When we read any scale, we are only allowed to guess or be uncertain about one place value.

To keep track of the accuracy of any calculation in science,

we must learn to count SIGNIFICANT FIGURES.

Sig.Figs.= the number of certain figures + one uncertain

examples:

Number                   SigFigs

0.204                            3

1.002                            4

0.0034                          2

1000                             1,2,3 or 4

2.00 x10⁴                     3

3005                             4

Practice Sheet

#7

a    6.3

b.  2.4x10^-4

c.  1.33

d.  1.3x10²

e.   6.4exp8x5exp5=    3. x10¹⁴

f.  5.11 x 10⁵

g.  202 or 2.02x10 ²

h.  9 x 10¹

i.  2 x 10 1

j.  1 x 10 -4

k. 2

l.  2.2 x 10 -6

Sig.Fig. Rule for Adding and Subtracting

First note that this rule is different from the x and / rule.

Example

2.34 + 0.6 = 2.94  or 3  both are incorrect using sig fig stuff.

First line up the decimal points and notice where the uncertainty is.

                     2.34

                     0.6

                   _____

                     2.94

The ones column is made of two certain numbers

The tenths column is certain + uncertain = uncertain.

The hundredths is uncertain + nothing = uncertain.

Therefore, we have our first uncertainty at the tenths column…

and must round off there.

Final answer = 2.9

(note use all numbers until the end and then round off to the correct sig. figs.)

Example 2

2.34 x 10¹  +  3.6 x 10²

                           23.4

                         360.

                         383.4  but uncertainty started at the tens column

          Answer to the correct sigfigs must be 3.8 x 10 ²

.0051 + 3 x 10 ¹

                       .0051

                   30.

Answer   3x10 1

Practice Sheet

#8 a – n

a.  12.1

b.  22.0

c.  0.09

d.  0.002

e.  0.322

f.   4.0621 x 10 ⁴

g.  5.213 x 10 ²

h.  7.97 x 10 ⁴

i.   5.26 x 10 ^-5

j.   4.84 x 10 ²

k.  1.2 x 10 ⁸

l.   4.21 x 10 ³

m.  95.00 or 9.500 x 10 ¹

n.  1 x 10 -2