Chapter 3: Scientific Measurement

Section 3.1 Scientific Notation Accuracy/Precision

Percent Error Significant Digits

Scientific Notation

• multiplier

5.68 x 105

Can be pos or neg

Always between 1 and 9.999

exponent

Scientific Notation – Try These

1) 5467 =

2) 401000 =

3) 0.0023 =

4) 0.127 =

Scientific Notation – Try These

1) 5467 = 5.467 x 103 (decimal Left – exp Larger)

2) 401000 = 4.01 x 105 (decimal Left – exp Larger)

3) 0.0023 = 2.3 x 10-3 (Number <1, then exp is <0)

4) 0.127 = 1.27 x 10-1 (Number <1, then exp <0)

Scientific Notation – Try These

1) 3.61 x 105 =

2) 4.2001 x 107 =

3) 3.54 x 10-3 =

4) 7.8 x 10-4 =

Scientific Notation – Try These

1) 3.61 x 105 = 361,000

2) 4.2001 x 107 = 42,001,000

3) 3.54 x 10-3 = 0.00354

4) 7.8 x 10-4 = 0.00078

Try this in your calculator

3.1 x 105

----------------------------

(6.03 x 104 * 9.23 x 10-7)

Try this in your calculator

3.1 x 105

----------------------------

(6.03 x 104 * 9.23 x 10-7)

5.5698395 x 106

5,569,839.5

Now try these two problems

(3.2 x 106 * 1.7 x 10-4) (3.05 x 10-2 * 4.5 x 104)

------------------------------ -------------------------------

(5.3 x 10-3 * 5.6 x 10-2) (6.02 x106 * 5.42 x 10-1)

Now try these two problems

(3.2 x 106 * 1.7 x 10-4) (3.05 x 10-2 * 4.5 x 104)

------------------------------ -------------------------------

(5.3 x 10-3 * 5.6 x 10-2) (6.02 x106 * 5.42 x 10-1)

1.832884 x 106 4.206 x 10-4

1.832,884 0.0004206

Measurements

• Every measurement MUST have 2 things:

1) a numeric value

2) a unit

Making Measurements

All your measurements should be both correct and reproducible

Making Measurements

• Accuracy – a measure of how close a measurement comes to the actual or true value of whatever is measured

– 100 C for boiling water

• Precision – a measure of how close a series of measurements are to one another

– Multiple measurements give same result

What does “accurate” look like?

What does “accurate” look like?

What does “precise” look like?

What does “precise” look like?

Percent Error

• Quantifies how accurate your measurement really is

Memorize! Memorize!

Memorize!

3 Rules for Sig Figs

• All non-zero digits (1-9) are significant – 14.567 has 5 sig figs

• Any zeroes between non-zeroes are significant – “Sandwich rule”

– 1.050607 has 7 sig figs

• IF there is a decimal point, THEN the trailing zeroes are significant – 10.000 has 5 sig figs

– 0.0300 has 3 sig figs

Zeroes that are not significant

• Zeroes to the left of a non-zero digit (leading zeroes) – 0.0034 has 2 sig figs (3.4 x 10-3)

– 0.0000001 has 1 sig fig (1 x 10-7)

• Zeroes to the right of number without a decimal point – 17000 has 2 sig figs

– 310 has 2 sig figs, but 310.0 has 4 sig figs

Adding and Subtracting with Sig Figs

• Step 1: add the numbers

• Step 2: round to the same number of decimal places as the measurement with the least number of decimal places

• 8.32 cm + 9.203 cm + 1.2 cm = 18. 723 cm

• ROUND to 1 decimal place: 18.7 cm

Exact Numbers

• Counted numbers have unlimited (or infinite) sig figs – 30 students

– 4 windows

• Conversion factors have unlimited (or infinite) sig figs – 60 s/1 min

– 1000 mL/1 L

• These do not count when you round

Exact Numbers

• You measure a time to be 4.31 min, but you want seconds

– Multiply by 60

• 4.31 min * 60 sec/min = 259 sec

– Keep 3 sig figs!