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Significant Figures

- Michelle H-duke
- Department of Chemistry/Biochemistry

Definitions

- Quantitative observations use the ability to

count and usually involve scientific instruments. - Qualitative observations do not use numbers.
- Base Units are specific units used for each

physical quantity. It is important that you

write the symbol correctly (m, g, l, , etc.) - Derived units are those that are multiples of

base units such as millimeter (mm).

Significant Figures

- Significant figures (often referred to as sig

figs) are used to tell how precisely the

measurements were taken. They are also an

indication of the precision of the instrument or

measuring device used in a particular

measurement. There are rules to be learned about

how to determine the number of sig figs. - It is the minimum number of digits needed to

write the given value without loss of accuracy

appropriate to the measurement or measuring

device.

- Scientific notation is used most often in the

sciences to express the degree of accuracy. It is

less commonly used in the maths and soft

sciences. - Example 145.5 has four sig figs. 1.455 X 102

but if you wrote it as 1.4550 X 102 it implies

that you know the value after the 5 which is not

the case in 145.5. - 1.4550 X 102 has five sig figs.
- If the degree of accuracy to be reported is less

than the number, rounding is required.

- Rules
- All non-zero numbers are significant
- -Example 1, 2, 3.
- Zeros are sometimes significant.
- a. Zeros between significant numbers are

significant. - -Example 2505 has 4 sig fig.
- b. Zeros at the end of a number to the right

of a decimal point are significant. - -Example 10.020450 has 8 sig fig.
- c. Zeros in numbers to the right of a decimal

not preceded by a whole number are not

significant. - -Example 0.0025 has 2 sig fig.
- The numbers used in conversion factors are not

included and are called exact numbers - -Example 1 inch 2.54 cm. Thus

in calc. 2.54 is not considered in the final

answer.

Rounding Off Look at the digits beyond the last

place desired -if the number is greater than 5

round to the next highest number -42.47354 to 3

sig figs 42.5 -if the number is less than 5

the leave the number the same, considered to be

rounding down -42.47354 to 4 sig figs

42.47 -In special cases where the number is

exactly halfway, round to the nearest even

digit. -42.47354 to 5 sig figs 42.474

Scientific/Exponential Notation

- 450000 can be written as 4.5 x 105
- 0.0000045 is the same as 4.5 x 10-6
- Problems
- 1. Express 7250000 in scientific notation.
- 25005 in scientific notation
- 625.25 in scientific notation
- 2. Expand 5.55 x 10-8.

Math Operations

- Multiply Multiply the bases and add the

exponents - Ex 2.5 x 102 x 1.2 x 105 3.0 x 107
- 2.5 x 102 x 1.2 x 10-5 3.0 x 10-3
- Division Divide the bases and subtract the

exponents - 2.5 x 102 / 1.2 x 105 2.08 x 10-3 ---gt 2.1 x

10-3 - 2.5 x 102 x 1.2 x 10-5 2.08 x 107--gt2.1 X 107

- Addition and subtraction
- Convert all of the numbers to the same power of

10 - Add/Subtract the numbers together and use the

common exponent - Example
- 255 3125 45025
- 255 x 102 31.25 x 102 450.25 x 102
- 736.50 x 102 ? 7.37 x 104 (justified)

Sig Figs. In Math Operations

- Addition and Subtraction
- Complete all of the addition or subtraction as

you normally would. Retain numbers in answer

until the final answer. The final answer should

contain the same number of digits to the right of

the decimal point as the measurement with the

least number of digits to the right of the

decimal. - Example 5.345
- 6.2227
- - 0.25
- 11.3177 ? 11.32 (units)

- Multiplication and Division
- When multiplying and dividing numbers, the final

answer should contain no more significant figures

than the fewest number of significant figures in

any of the numbers being multiplied or divided in

the calculation. - Example 175 x 3126 x 25 1367625 (units)
- There are only 2 sig figs in the least so the

answer should be reported as 1400000

Note When using scientific notation, the power

of 10 has no influence on the figures to be

retained. Example 3.26 x 10-5 x 1.78 5.80 x

10-5 4.3179 x 1012 X 3.6 x10-19 1.6 x10-6

Note units should always be included as it gives

information of the magnitude as well as the

degree of accuracy of the measurement. When

doing conversions, the conversion factor is not

considered when determining significant

figures. Example How many centimeters are in

82.00 inches? 1 inch 2.54 cm 1 in/2.54 cm

82.00/x x 208 cm Since 82.00 has 4 sig fig.

Your answer should be reported as 208.0 cm.

SI Prefixes

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