Significant FiguresSignificant Figures

Unit 1 Presentation 3Unit 1 Presentation 3

Scientific NotationThe number of atoms in 12 g of carbon:

602,200,000,000,000,000,000,000

6.022 x 1023

The mass of a single carbon atom in grams:

0.0000000000000000000000199

1.99 x 10-23

N x 10n

N is a number between 1 and 10

n is a positive or negative integer

Scientific Notation568.762

n > 0

568.762 = 5.68762 x 102

move decimal left

0.00000772

n < 0

0.00000772 = 7.72 x 10-6

move decimal right

Addition or Subtraction

1. Write each quantity with the same exponent n

2. Combine N1 and N2 3. The exponent, n, remains

the same

4.31 x 104 + 3.9 x 103 =

Scientific Notation

Multiplication

1. Multiply N1 and N2

2. Add exponents n1 and n2

(4.0 x 10-5) x (7.0 x 103) =

Division

1. Divide N1 and N2

2. Subtract exponents n1 and n2

8.5 x 104 ÷ 5.0 x 109 =

Significant figures (sig figs)Significant figures (sig figs)

How many numbers in a measurement mean How many numbers in a measurement mean somethingsomething

When we measure something, we can (and do) When we measure something, we can (and do) always estimate between the smallest marks.always estimate between the smallest marks.

21 3 4 5

Significant figures (sig figs)Significant figures (sig figs)

The more marks the better we can The more marks the better we can estimate.estimate.

Scientists understand that the last number Scientists understand that the last number measured is actually an estimatemeasured is actually an estimate

21 3 4 5

Sig FigsSig Figs

What is the smallest mark on the ruler that What is the smallest mark on the ruler that measures 142.15 cm?measures 142.15 cm?

142 cm?142 cm?

140 cm?140 cm?

Here there’s a problem: Does the zero count Here there’s a problem: Does the zero count or not?or not?

Scientists needed a set of rules to decide Scientists needed a set of rules to decide which zeroes count.which zeroes count.

All other numbers All other numbers alwaysalways count count

Which zeros count?Which zeros count?

Leading zeros never countLeading zeros never count– 0.045 0.045

Trapped zeros always countTrapped zeros always count– 100365405.057100365405.057

Trailing zeros only count if there is a Trailing zeros only count if there is a decimal place presentdecimal place present– 12400 Here the zeroes do NOT count12400 Here the zeroes do NOT count– 12400. Here the zeroes DO count12400. Here the zeroes DO count

Sig FigsSig Figs

Only measurements have sig figs.Only measurements have sig figs.

Counted numbers are always exactCounted numbers are always exact– A dozen is exactly 12A dozen is exactly 12

A a piece of paper is measured 11 inches A a piece of paper is measured 11 inches tall.tall.

Being able to locate, and count significant Being able to locate, and count significant figures is an important skill.figures is an important skill.

Sig figs.Sig figs.

Count the sig figs and the number of significant Count the sig figs and the number of significant zeros in the following numberszeros in the following numbers– 458 g458 g– 4085 g4085 g– 4850 g4850 g– 0.0485 g0.0485 g– 0.004085 g0.004085 g– 40.004085 g40.004085 g

Adding and subtracting with Adding and subtracting with significant figuressignificant figures

The last significant figure in a The last significant figure in a measurement is an estimate.measurement is an estimate.Your answer can not be better (more Your answer can not be better (more precise) than your worst (least-precise) precise) than your worst (least-precise) estimate. estimate. You have to round it to the least place of You have to round it to the least place of precision of the measurement in the precision of the measurement in the problemproblem

For example

27.93 6.4+ First line up the decimal places

27.936.4+

Then do the adding

34.33Find the estimated numbers in the problem

27.936.4

This answer must be rounded to the tenths place

PracticePractice

4.8 + 6.87654.8 + 6.8765520 + 94.98520 + 94.980.0045 + 2.1130.0045 + 2.1136.0 x 106.0 x 1022 - 3.8 x 10 - 3.8 x 1033 5.4 - 3.285.4 - 3.286.7 - .5426.7 - .542500 -126500 -126

6.0 x 106.0 x 10-2-2 - 3.8 x 10 - 3.8 x 10-3-3

Multiplication and DivisionMultiplication and Division

Rule is simplerRule is simpler

Answer will have the same number of sig figs as Answer will have the same number of sig figs as the the value with thevalue with the least number of sig figs in least number of sig figs in the problemthe problem

3.6 x 653 = 2350.83.6 x 653 = 2350.8

3.6 has 2 s.f. 653 has 3 s.f.3.6 has 2 s.f. 653 has 3 s.f.

answer can only have 2 s.f.answer can only have 2 s.f.

24002400

Note that there is NO decimal point present!Note that there is NO decimal point present!

Multiplication and DivisionMultiplication and Division

Same rules for divisionSame rules for division

Lets do some practice.Lets do some practice.

4.5 / 6.2454.5 / 6.245

4.5 x 6.2454.5 x 6.245

9.8764 x .0439.8764 x .043

3.876 / 19833.876 / 1983

16547 / 71416547 / 714