Sig FigsThe Saga

• In a galaxy far, far away, a bunch of students were arguing whether there was a difference between two measurements.

20.4 cm and 20.40 cm

Reading measuring instruments to their limit

• You can only be as precise as your measuring instrument allows you to be.

• Ex.

Other examples:• How much fluid is in this

graduated cylinder? (73.0 ml)

What is the temperature? (38.45 oC)

What are Significant Figures?(as opposed to significant figurines...)

• Sig figs help us understand how precise measurements are.

• Using sig figs increases accuracy and precision.• Sig figs cut down on error caused by improper

rounding.

HOORAY FOR

SIG FIGS!!! SIG FIGS RULE

So… which digits are significant?• Rule #1:

– All non-zero digits are significant.• 24 has two sig figs, 24.1 has 3 sig figs

• Rule #2:– All zeros bounded by non-zero integers are

significant• 2004 has four sig figs• 20.04 also has 4 sig figs

So… which digits are significant?

• Rule #3:– Zeros placed before other digits (leading zeros)

are not significant• 0.024 has 2 sig figs

• Rule #4:– Zeros at the end of a number are significant

ONLY if they come after a decimal point• 2.40 has three sig figs• 240 only has 2 sig figs

Practice:• How many sig figs?

» 409.25 o 0.050» 83 o 300 900» 98.207 o 5.5 x 102

» 0.001 o 45.030» 4.3 x 102 o 35 000» 0.003050 o 0.00400» 4200 o 16.8090» 0.9106 o 460 090» 0.200 o 150 000 000

Rules for Addition and Subtraction

• In an addition or subtractions,– answers must be rounded to the same

decimal place (not sig figs) as the least number of decimal places in any of the numbers being added or subtracted

– Ex. 2.42 + 14.2 + 0.6642

– Ex. 2.42 + 14.2 + 0.6642• Step 1 line them up

2.42 14.2 +0.6642 17.2842

• Step 2: round to 3.3, because 0.2 only has one decimal place

The answer is 17.3

Ex 1- 6.25 + 4.350 + 15.809 = 26.409

becomes 26.41 WHY

Ex 2-14.4 + 12.0 - 5 = 21.4

becomes 21 WHY

Ex 3-589.090 + 0.04 + 78.890 = 668.02

becomes668.02 WHY

Ex 4-33.2306 + 5.050 + 0.00604 = 38.28664 becomes38.287 WHY

Rules for Multiplication and Division

• The number of sig figs in the answer should be the same as in the number with the least sig figs being multiplied or divided.

– Ex. 7.3 x 1264 = 9227.2» The answer must only contain 2 sig figs, so we

use scientific notation»The answer becomes 9.2 x 103

»This answer contains 2 sig figs

Ex 1-15.0 x 4.515 x 1376 = 931 896

becomes9.32 x 105 WHY

Ex 2-0.003 x 0.050 x 0.04 = 0.000006

becomes0.000006 = 6 x 10-6 WHY

Ex 3- 45.56 x 134.04 x 0.340 = 2076.333216

becomes2.08 x103 WHY

Ex 4-34.56 x 14 x 134.020 = 64844.2368

becomes6.5 x 104 WHY

Adding and multiplying numbers in a word problem

1- Set up numbers according to the word problem

2- Solve using order of operations3- At each step give the answer in sig figs4- Convert final answer to sig figs

Ex 1. 4.67 + 8.953 + 0.652 765.32 x 8.9

- 4.67 + 8.953 + 0.652 = 14.275 becomes 14.28

- 765.32 x 8.9 = 6811.348becomes 6.8 x 103

- 14.28/6.8 x 103 = 0.0021becomes 0.0021 =

2.1x10-3

Ex 2 6.8 + 5.80 x 8.0 x 0.06 - 7.8700.0800

- 6.8 +(5.80 x 8.0 x 0.06) - 7.870 0.0800- 6.8 + (2.784) - 7.870 which becomes

0.0800- 6.8 + 3 – 7.870

0.0800- 1.93 which becomes

0.080020.0800 = 25 becomes

30 why

Exceptions and specialcircumstances

• Adding and scientific notation (5.8 x 102) + 368

4.87 x 105

When adding in using SN, the exponents must be the same.

You have 2 options to solve the problem. 1- Convert 5.8 x102 to 580 and get rid of the exponent580 + 368

2- Convert 368 to the same exponent so it becomes 3.68 x 102

5.8 x 102 + 3.68 x 102

Both are correct, but option 1 is easier

• Rounding off and keeping a zero as a significant digit

8253.0569 = 649.847 12.7In this example you must keep 3 sig figs in your answer.When rounding off 649.847 should become 650.

Problem, 650 only has 2 sig figsSolution: put a – above the zero, this makes it

significant,650 will become your answer.

• Having many insignificant zero’s and additionWhen adding the following: 136.2 + 2 500 000 + 14.01 We get 2 500 150.21 which should become 2 500 150.

EXCEPT, we have to use sig figs, and the addition rule says that

we must round to the least precise decimal place. Therefore, because 2 500 000 is only precise to the hundredthousands place, we need to round the answer to 2 500 000.

This is true for any additions that end in non sig. zero’s. ex- 5 500 + 15 = 55 15 but becomes 5500310 + 6 = 316 but becomes 320259 500 + 1670 + 23 = 261 193 but becomes 261 200

• Converting units

When converting units, sig figs need to be maintained.

Ex 1- 4.0 cm to m becomes 0.040 not 0.04Ex 2- 1250 mL becomes 1.25 L not 1.250

Solve the following:5.3 x 4.2 + 1.502.5 + 8.163 x 5.67(5.3 x 4.2) + 1.50 = (22.26) + 1.50 = 2.5 + (8.163 x 5.67) 2.5 + (46.28421)

22 + 1.50 = 23.50 becomes2.5 + 46.3 48.824 = 0.4918032 which becomes48.80.49

(6.42 x 105) x (0.45 x 10-3) + 56.5 + 150.03

(6.42 x 105) x (0.45 x 10-3) + 56.5 + 150.03 = (288.9) + 56.5 + 150.03 = (2.8 x 102 ) + 56.5 + 150.03 = 280 + 56.5 + 150.03 =486.53 which becomes487 which becomes490Holy cow, zero’s have become the enemy!!

Your next assignment is hand in a2000word essay on the history andimportance of significant figures and how

they positively affect our everyday lives.

Due date- 2 weeks

Psych-Why would I want to correct 96 essays

on significant figures?????