1

Scientific measurement

2

Types of measurement Quantitative- use numbers to describe Qualitative- use description without

numbers 4 feet extra large Hot 100ºF

3

How good are the measurements?

Scientists use two words to describe how good the measurements are

Accuracy- how close the measurement is to the actual value

Precision- how well can the measurement be repeated

4

Differences Accuracy can be true of an individual

measurement or the average of several Precision requires several

measurements before anything can be said about it

examples

5

Let’s use a golf anaolgy

6

Accurate? No

Precise? Yes

7

Accurate? Yes

Precise? Yes

8

Precise? No

Accurate? No

9

Accurate? Yes

Precise? We cant say!

10

1. Significant Figures Indicate precision of a measurement.

Recording Sig Figs–Sig figs in a measurement include the

known digits plus a final estimated digit

2.35 cm

11

2. NON-ZEROs - significantAll NON-Zeros are SIGNIFICANT

–1, 2, 3, 4, 5, 6, 7, 8, & 9–There are ____Sig figs in the measurement

below?Answer?= 3

2.35 cm

12

Rules for determining which ZEROs are significant

3. “SANDWICHED” zeros - significant– Zeros between other nonzero(1,2,3…)

digits are significant• 50.3 has three sig fig• 3.0025 has five sig fig

13

Rules for determining which ZEROs are significant

4. “BEGINNING” Zeros – not significant

– Zeros in front of the 1st nonzero digit are NOT significant

• 0.892 has three sig fig• 0.0008 has one sig fig

14

Rules for determining which ZEROs are significant

5. ENDING zeros – significant or not significant?– Ending zeros in a number without a decimal -

not significant• 1000 has one sig fig

– Ending zeros in a number with a decimal - significant

• 57.00 has four sig fig• 2.000000 has seven sig fig• 56700. has five sig fig

15

Sig Figs Only measurements have sig figs. Counted numbers are exact A dozen is exactly 12 A a piece of paper is measured 11

inches tall. Being able to locate, and count

significant figures is an important skill.

16

Sig figs.How many sig figs in the following

measurements? 458 g 4085 g 4850 g 0.0485 g 0.004085 g 40.004085 g

17

Sig Figs. 405.0 g 4050 g 0.450 g 4050.05 g 0.0500060 g Next we learn the rules for calculations

18

6. Add/Subtract ––The final answer should be rounded to

have the same number of decimal places as the measurement with the smallest number of decimal places.

3.75

+ 4.1_

7.85

224

+ 130

354 7.9 350

3.75

+ 4.1

7.85

224

+ 130

354

19

6. Multiply/Divide ––The final answer has the same number of

significant figures as the measurement having the least number of sig figures.

(13.91)(23.3) = 324.103

324

4 SF 3 SF 3 SF

20

7.Rounding?–Always reduce to significance by

Rounding when you’ve finished and reached the end of the whole problem.

213.67 - 98 = 115.67

116 round up

Calculator answer

No decimal places

Check addition Rule (least # of decimal places), then round

no decimal places

2 decimal places

21

7.Rounding?–Always reduce to significance by

Rounding when you’ve finished and reached the end of the whole problem.

7.32(8.189) = 59.94348

59.9 rounded down

Calculator answer

3 sf3sf 4sf

Check multiple rule (least # of sigfig), then round

22

Rounding rules look at the number behind the one

you’re rounding. If it is 0 to 4 don’t change it If it is 5 to 9 make it one bigger round 45.462 to four sig figs to three sig figs to two sig figs to one sig fig

23

Practice 4.8 + 6.8765 520 + 94.98 0.0045 + 2.113 6.0 x 102 - 3.8 x 103 5.4 - 3.28 6.7 - .542 500 -126 6.0 x 10-2 - 3.8 x 10-3

24

Multiplication and Division 4.5 / 6.245 4.5 x 6.245 9.8764 x .043 3.876 / 1983 16547 / 714