Sig FigsSig FigsSignificant FiguresSignificant Figures

What are Sig Figs?What are Sig Figs? I read in the paper that Randy Lerner (owner I read in the paper that Randy Lerner (owner

of the Browns) is worth 1.7 billion dollars.of the Browns) is worth 1.7 billion dollars. Myself and a friend bought 4 tickets for Myself and a friend bought 4 tickets for

$264.30$264.30 Assume Randy Lerner gets every penny of Assume Randy Lerner gets every penny of

that and hasn’t had another expense yet, that and hasn’t had another expense yet, does that mean Randy Lerner now has does that mean Randy Lerner now has exactly $1,700,000,264.30?exactly $1,700,000,264.30?

Of course not, all of those 0’s were actually Of course not, all of those 0’s were actually numbers that we didn’t report because we numbers that we didn’t report because we couldn’t measure accurately enough. The couldn’t measure accurately enough. The number was rounded!number was rounded!

This is where sig figs come into This is where sig figs come into playplay

Absolutely accurate measurements are Absolutely accurate measurements are impossible!!!impossible!!!

We must round somewhereWe must round somewhere When we do calculations with these When we do calculations with these

numbers we must reflect how accurate our numbers we must reflect how accurate our initial numbers were.initial numbers were.

A significant digit means that digit was A significant digit means that digit was accurately measuredaccurately measured

An Insignificant digit means that digit was An Insignificant digit means that digit was NOT accurately measured.NOT accurately measured.

Rules for determining if a Rules for determining if a digitdigit is significant is significant

1.1. If it is not a zero, it is significant.If it is not a zero, it is significant.1231232.2. If a zero is between two significant If a zero is between two significant

digits, it is significant. digits, it is significant. 3093093.3. Zeros at the end of a number with a Zeros at the end of a number with a

decimal point are significant. decimal point are significant. 56.056.0 4.4. Zeros at the end of a number that do Zeros at the end of a number that do

not have a decimal point are NOT not have a decimal point are NOT significant. significant. 8240082400

5.5. Zeros at the front of a decimal are NOT Zeros at the front of a decimal are NOT significant. significant. .00562.00562

Determine how many sig figs Determine how many sig figs are in each numberare in each number

734734 100,025100,025 65010006501000 .00034.00034 2.000342.00034 527.00527.00 16.0116.01 1870000000000018700000000000

33 66 44 22 66 55 44 33

Round each number to the Round each number to the given number of sig figsgiven number of sig figs

(2) 734(2) 734 (4) 101.025(4) 101.025 (3) 651500(3) 651500 (5) .00334(5) .00334 (4) 132.084(4) 132.084 (3) 527.00(3) 527.00 (5) 16.01(5) 16.01 (3) 18700(3) 18700

730730 101.0101.0 652000652000 .0033400.0033400 132.1132.1 527527 16.01016.010 1870018700

How to report answersHow to report answers When multiplying or When multiplying or

dividing.dividing. You can only have You can only have

as many sig figs in as many sig figs in your answer as you your answer as you do in the number do in the number with the least amount with the least amount of sig figs.of sig figs.

3.56 x 2.1= 3.56 x 2.1= 7.4767.476 7.57.5 (2 sig figs) (2 sig figs)

When adding or When adding or subtracting.subtracting.

Numbers added to or Numbers added to or subtracted from subtracted from insignificant numbers are insignificant numbers are insignificant (rounded insignificant (rounded off).off).

347.58 347.58 + 21+ 21

368.58368.58 369369

insignificant

Scientific NotationScientific Notation some numbers so large or small that is a some numbers so large or small that is a

pain to write out normallypain to write out normally for example $1,700,000,000for example $1,700,000,000 To write in scientific notation write down all To write in scientific notation write down all

sig figs x10sig figs x10xx

The number is always written to the The number is always written to the ones ones placeplace with a decimal with a decimal

The number it is raised to is the number of The number it is raised to is the number of places you need to move to the decimal.places you need to move to the decimal.

so the above number is $1.7x10so the above number is $1.7x1099

Quick conversionsQuick conversions

6.7 x106.7 x10-7-7

2.31 x102.31 x1055

5.79 x105.79 x1033

4.19 x104.19 x10-5-5

.0065.0065 94,100,00094,100,000 .000000065.000000065 9,8409,840

.00000067.00000067 231000231000 57905790 .0000419.0000419 6.5 x106.5 x10-3-3

9.41 x109.41 x1077

6.5 x106.5 x10-8-8

9.84 x109.84 x1033