SIGNIFICANT FIGURES

ACCURACY VS. PRECISION In labs, we are concerned by how

“correct” our measurements are They can be accurate and precise

Accurate: How close a measured value is to the actual measurement

Precise: How close a series of measurements are to each other

EXAMPLE The true value of a measurement is

23.255 mL Below are a 2 sets of data. Which one

is precise and which is accurate?1. 23.300, 23.275, 23.2352. 22.986, 22.987, 22.987

SCIENTIFIC INSTRUMENTS In lab, we want our measurements to be

as precise and accurate as possible For precision, we make sure we calibrate

equipment and take careful measurements

For accuracy, we need a way to determine how close our instrument can get to the actual value

SIGNFICANT FIGURES We need significant figures to tell us

how accurate our measurements are The more accurate, the closer to the

actual value Look at this data. Which is more

accurate? Why? 25 cm 25.2 cm 25.22 cm

ANSWER 25.22cm

The more numbers past the decimal (the more significant figures), the closer you get to the true value.

How do we determine how many significant figures are in different pieces of lab equipment?

SIGNIFICANT FIGURES Significant figure – any digit in a

measurement that is known for sure plus one final digit, which is an estimate Example:

4.12 cmThis number has 3 significant figuresThe 4 and 1 are known for certainThe 2 is an estimate

SIGNIFICANT FIGURES In general: the more significant figures

you have, the more accurate the measurement

Determining significant figures with instrumentation Find the mark for the known

measurements Estimate the last number between marks

SIGNIFICANT FIGURES Try these:

Graduated cylinderTriple Beam balanceRuler

RULES FOR SIGNIFICANT FIGURES

Rule 1: Nonzero digits are always significant

Rule 2: Zeros between nonzero digits are significant 40.7 (3 sig figs.) 87009 (5 sig figs.)

Rule 3: Zeros in front of nonzero digits are not significant 0.009587 (4 sig figs.) 0.0009 (1 sig figs.)

RULES FOR SIGNIFICANT FIGURES

Rule 4: Zeros at the end of a number and to the right of the decimal point are significant85.00 (4 sig figs.)9.070000000 (10 sig figs.)

Rule 5: Zeros at the end of a number are not significant if there is no decimal40,000,000 (1 sig fig)

RULES FOR SIGNIFICANT FIGURES

Rule 6: When looking at numbers in scientific notation, only look at the number part (not the exponent part) 3.33 x 10-5 (3 sig fig) 4 x 108 (1 sig fig)

Rule 7: When converting from one unit to the next keep the same number of sig. figs. 3.5 km (2 sig figs.) = 3.5 x 103 m (2 sig

figs.)

HOW MANY SIGNIFICANT FIGURES?

1. 35.02

2. 0.0900

3. 20.00

4. 3.02 X 104

5. 4000

ANSWERS1. 4

2. 3

3. 4

4. 3

5. 1

ROUNDING TO THE CORRECT NUMBER OF SIG FIGS.

Many times, you need to put a number into the correct number of sig figs.

This means you will have to round the number

EXAMPLE: You start with 998,567,000 Give this number in 3 sig figs.

ANSWER Step 1: Get the first 3 numbers (3 sig

figs.) 998

Step 2: Check to see if you have to round up or keep the number the same You need to look at the 4th number 9985

If the next number is 5 or higher, round up

If the next number is 4 or less, stays the same

Therefore = 999

ANSWER Step 3: Take your numbers and put the

decimal after the first digit 9.99

Step 4: Count the number of places you have to move to get to the end of the number and put it in scientific notation. 9.99 x 108

NOTE: If the number is BIG it will be a positive exponent. If the number is a DECIMAL, it will be a negative exponent.

OTHER POSSIBILITY Example:

999,999,999 (3 sig. figs.) When you take the first three numbers,

you get 999

But when you round, it is going to round from 999 1000

Therefore, the number becomes: 1.00 x 108

TRY THESE

1. 10,000 (3 sig. figs.)2. 0.00003231 (2 sig. figs.)3. 347,504,221 (3 sig. figs.)4. 0.000003 (2 sig. figs.)5. 89,165,987 (3 sig. figs.)