Significant Figures in measurements and calculations

significant figures objective

I can determine precision of a number using “sig figs”

I can calculate using the correct precision i.e. correct “sig figs”

Significant Figures in Measurements What are Significant Figures? Significant Figures convey important

information about the precision of a measurement.

In measurements, Significant Figures are all the digits that can be known precisely in a measurement, plus a last estimated digit.

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Significant Figures in Measurements

In measurements, the significant figures are all the digits that are known, plus a last digit that is estimated.

Volume in the graduated cylinder

__________ ml

Metric Ruler Sig FigsOn a metric ruler, the smallest divisions are millimeters, 0.1 cm or 0.001m. Rarely does the object end neatly on one of the lines of the instrument, but that forces the use of measurement zeros.

13.30 cmTo indicate that the object being measured ends exactly at the third line after the 13, we must write 13.30 cm. This indicates that, to our best estimation, the measurement does not extend into the hundredth of the centimeter.

Metric ruler sig figs

A. 14 cmB. 14.0 cmC. 14.00 cmD. 14.000 cm

If the object ends exactly at the 14 cm line, we must add two zeros to the end.

14.00 cm

Metric ruler sig figsA. 12.3 cmB. 12.37 cmC. 12.80 cmD. 12.84 cmE. 12.85 cmF. 12.86 cmG. 12.87 cmH. 12.7 cmI. 12.8 cmJ. 13.86 cm

Most of the time, our measurements fall between the lines and, we must make agonizing estimates about where the measurement does fall.

12.85 cm

Thermometer Sig figs

In measurements, the significant figures are all the digits that are known, plus a last digit that is estimated.

______ oC ______ oC68.0 -1.1

Triple beam balance sig figs

A. 9 gB. 9.0 gC. 9.04 gD. 9.05 gE. 19 gF. 19.0 gG. 19.04 gH. 19.05 gI. 19.06 gJ. 19.1 g

In measurements, the significant figures are all the digits that are known, plus a last digit that is estimated.

19.04 g

Rules for writing and reading sig figs In order to present results with the proper

precision, we need to know how many significant figures are present in each number we use in a calculation.

There are four basic rules: 1. The digits 1 - 9 always count.2. Zeroes between the digits 1 - 9 always

count. 3. Zeroes in the beginning of a number never

count. 4. Zeroes at the end of a number count only if

there is a written decimal point.

Rules for writing and reading sig figs1. The digits 1 - 9 always count.2. Zeroes between the digits 1 - 9 always

count. 3. Zeroes in the beginning of a number never

count. 4. Zeroes at the end of a number count only if

there is a written decimal point.

Rule #1 examples: 24.7cm, 0.743 cm, 714 cm

All have three sig figs

Rules for writing and reading sig figs1. The digits 1 - 9 always count.2. Zeroes between the digits 1 - 9 always

count. 3. Zeroes in the beginning of a number never

count. 4. Zeroes at the end of a number count only if

there is a written decimal point.

Rule #2 Examples: 7003 cm, 40.79 cm, 1.503 cm

all have 4 sig figs

Rules for writing and reading sig figs1. The digits 1 - 9 always count.2. Zeroes between the digits 1 - 9 always

count. 3. Zeroes in the beginning of a number never

count. 4. Zeroes at the end of a number count only if

there is a written decimal point.

Example: 0.00701cm, 0.422cm, 0.00000909cm

all have 3 sig figs

Hey!!! You can get rid of these place holding zeros by using scientific notation

7.01x10-3cm 4.22x10-1cm 9.09x10-6cm

Rules for writing and reading sig figs1. The digits 1 - 9 always count.2. Zeroes between the digits 1 - 9 always

count. 3. Zeroes in the beginning of a number never

count. 4. Zeroes at the end of a number count only if

there is a written decimal point.

Rule 4 Examples: 43.00cm, 1.010 mm, 9.000 mm

All have 4 sig figs

Tricky Rule 4 Examples: the zeros in 300cm, 7000km and 210m are not significant

Ambiguity (doubt, uncertainty) about precision can be avoided by using scientific notation 3.00x102cm 7.000x103km 2.1x102m

Rules for writing and reading sig figs Two situations have unlimited sig figs

a) counting example: there are 28 desks in the classroom

b) defined quantities example: 60minutes = 1 hour

1000 grams = 1 kilogram7 days = 1 week

Enter answers in your notes too!!1. Sig figs in 31.45 mL ?A. 0B. 1C. 2D. 3E. 4F. 5G. unlimited

31.45 mL

Rule 1: The digits 1 - 9 always count.

Enter answers in your notes too!!2. Sig figs in 150.53 g ?A. 0B. 1C. 2D. 3E. 4F. 5G. unlimited

150.53 mL

Rule 2: Zeroes between the digits 1 - 9 always count.

Enter answers in your notes too!!3. Sig figs in 40.00 mL ?A. 0B. 1C. 2D. 3E. 4F. 5G. unlimited

40.00 mL

Rule 4: Zeroes at the end of a number (trailing zeros) count only if there is a written decimal point.

Has NOTHING to do with where the decimal is located !!!

Enter answers in your notes too!!4. Sig figs in 0.056 mL ?A. 0B. 1C. 2D. 3E. 4F. 5G. unlimited

0.056 mL

Rule 3: Zeroes in the beginning of a number never count.i.e. leading zeros do not count

Enter answers in your notes too!!5. Sig figs in 10.10 g ?A. 0B. 1C. 2D. 3E. 4F. 5G. unlimited

Enter answers in your notes too!!6. Sig figs in 1.5 L ?A. 0B. 1C. 2D. 3E. 4F. 5G. unlimited

Enter answers in your notes too!!7. Sig figs in 8 yard TD pass?A. 0B. 1C. 2D. 3E. 4F. 5G. unlimited

Enter answers in your notes too!!8. Sig figs in 220 miles to Dallas A. 0B. 1C. 2D. 3E. 4F. 5G. unlimited

220 miles

Rule 4: Zeroes at the end of a number (trailing zeros) count only if there is a written decimal point.

Has NOTHING to do with where the decimal is located !!!

Enter answers in your notes too!!9. Sig figs in 12 donuts in a dozen? A. 0B. 1C. 2D. 3E. 4F. 5G. unlimited

There are always exactly 12 in a dozen.

Defined quantities and counting items have unlimited sig figs.

Practice 31.45mL has 4 sig figs 150.53g has 5 sig figs 40.00mL has 4 sig figs 0.056 seconds has 2 sig figs 10.10g has 4 sig figs 1.5L has 2 sig figs 8 yard touchdown pass has 1 sig fig 220 miles to Dallas has 2 sig figs 12 donuts in a dozen has unlisig figs

Practice 31.45mL has 4 sig figs 150.53g has 5 sig figs 40.00mL has 4 sig figs 0.056 seconds has 2 sig figs 10.10g has 4 sig figs 1.5L has 2 sig figs 8 yard touchdown pass has 1 sig fig 220 miles to Dallas has 2 sig figs 12 donuts in a dozen has unlimited sig figs

Significant Figures in Calculations

Multiplication and Division round to the same number of significant figures as the

measurement with the least number of significant figures

2.4526 meters÷ 8.4 meters0.29197619 meter

8.4 meters has two significant figures

= 0.29 meter

or 2.9×10-1 meter

An answer cannot be more precise than the least precise measurement from which it was calculated.

Significant Figures in Calculations Addition and Subtraction

Convert numbers to same exponent and align the decimal points, then

Round to the same number of decimal places as the least number of decimal places.

12.52 meters 349.0 meters+ 8.241 meters 369.761 meters

349.0 meters has the least number of digits (one) to the right of the decimal point.

Thus the answer must be rounded to one digit after the decimal point.

The correct rounded answer is 369.8 meters or 3.698 X 102

meters

Significant Figures in Calculations

An answer cannot be more precise than the least precise measurement from which it was calculated.

Once you know the number of significant figures your answer should have, you must round to that many digits, counting from the left.

16

feet

11 feet

What is the calculated area of your college dorm room to the correct number of significant figures?

Professor Harris reports his results to the correct number of sig figs.

Practice:1. 5.263L + 9.4L

2. 20s - 4.52s

3. 120g X 7.000mL

4. 1.20x102g X 8.000mL

5. 1000.0g / 3.12L

6. 1000g / 3.12L

Practice: answers with sigfigs underlined

1. 5.263L + 9.4L = 14.663 = 14.7 L2

2. 20s - 4.52s = 15.48s = 15s

3. 120g X 7.000 mL = 840 = 8.4x102

gmL

4. 1.20x102g X 8.000mL = 960. gmL

or 9.60x102 gmL

5. 1000.0g / 3.12L = 320.5128 = 321

or 3.21x102 g/L

6. 1000g / 3.12L = 320.5128 = 300 or

3x102 g/L

Another interesting defined quantityThe speed of light (usually denoted c) is a physical

constant. For much of human history, it was not known whether

light was transmitted instantaneously or simply very quickly.

Its value is now defined to be exactly 299,792,458 meters per second. It has unlimited sigfigs!! 299,792,458.0000000000000000000000000000…….…2.99792458 x 108 in scientific notation

How did they do that?In 1983, the meter was redefined in the International

System of Units (SI) as the distance traveled by light in vacuum in 1⁄299,792,458 of a second.

As a result, the value of c in meters per second is now fixed exactly by the definition of the meter.