Significant Digits and Scientific Notation

SNC 1DY

Learning GoalsBy the end of today’s lesson, you will be able

to count sig figs and express the appropriate amount of sig figs in a mathematical answer

By the end of today’s lesson, you will be able to convert standard notation to scientific notation, and vice versa

Significant Digits (Sig figs)In science, we make quantitative

observations – observations that require numbers and measurements.

All measurements have a certain amount of uncertainty associated with them

1) Significant Digits in MeasurementThe number of significant digits in

measurement is defined as all certain digits plus the first uncertain (or estimated) digit.

The measured value has three certain digits (1, 5, and 6) and one uncertain digit (5, or is it 4 or 6?). We say that the measurement has four significant digits.

Significant Figure RulesRule Example Significant

Figures

1. Nonzero digits are always significant

1.254 4 sig. fig.

2. Leading zeros (zeros before any nonzero digits) are NOT significant

0.000124 3 sig. fig.

3. Embedded zeros are significant

305.04 5 sig. fig.

4. Zeros’ behind the decimal point are significant

124.00 5 sig fig

State the number of significant figures in each of the followings: Measurement S.F. Measurement S.F.a. 967 e. 3.254

b. 1.034 f. 9.3

c. 1.010 g. 2.008

d. 5 h. 8.21

Rules for Sig Figs In Mathematical Operations

Multiplying and Dividing NumbersIn a calculation involving multiplication or division,

the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied or divided.

Ex. 9.0 x 9.0 =8.1 x 101, while 9.0 x 9 and 9 x 9 = 8 x 101

Rules for Sig Figs In Mathematical Operations

Adding and Subtracting NumbersWhen quantities are being added or subtracted,

the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.

e.g. 2.0 + 2.03 = 4.0

Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm0.04742 cm2 0.05 cm2

710 m ÷ 3.000 s 236.6666667 m/s 237 m/s

1818.2 lb x 3.231 ft 5872.786 lb·ft 5873 lb·ft

1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Scientific NotationA method used to express really big or really

small numbers. Consist of two parts:2.34 x 103

The first part of the number indicates the number of significant figures in the value.

The second part of the number DOES NOT count for significant figures.

This number is ALWAYS between 0 and 10

The 2nd part is always 10 raised to an integer exponent

How its Done1. Place the decimal point between the first

and second whole number, and write ‘x 10’ after the number.e.g. For 12345, it becomes 1.2 x 10e.g. For 0.00012345, it also becomes 1.2 x 10

2. Indicate how many places you moved the decimal by writing an exponent on the number 10.

a) A move to the left means a positive move.e.g. For 12345, it becomes 1.2 x 104

b) A move to the right means a negative move.e.g. For 0.00012345, it becomes 1.2 x 10-4

Success CriteriaAnswer questions on pg. 74 – 77 of

Extensions PackageAnswer questions on pg. 8 – 10 of Handout