Significant Figure and Scientific Notation Review

Significant Figure and Scientific Notation Review

Observations in Science

• We have two types of observations in Science: 

• Qualitative observations: observations made with the 5 senses. These observations do not include measurements, they are just characteristics. Example: The steel wool turned a dark grey color. 

• Quantitative observations: observations that include numbers and measurements. ALWAYS INCLUDE UNITS! :) Example: The steel wool was 4.86 grams.

Multiple Choice

Which of the following is an example of a Quantitative observation:

• The color of the substance is green.

• The substance smells like warm cookies.

• The substance feels like sandpaper.

• The substance has a mass of 2.34 grams

Quantitative Observations or measurements

• These measurements all have error! We observed this in our multiple massing experiment. Even though the mass of the object SHOULD NOT change, our measurements had variations. 

• On a measurement tool, there are always known or accurate digits and one estimated digit at the end of the measurement. 

• For example, if the balance reads 10.04 grams the 10.04 represents the estimated digit.

Multiple Choice

Which of the following digits is the ESTIMATED digit in the measurement, 44.567 grams:

• The first 4 in 44

• 5

• 6

• 7

Accuracy and Precision

• In measurement, we use two terms to describe the quality of the measurements: 

  Accuracy:

• Accurate measurements are close to the “true value” or true measurement. 

• Precision: Precise measurements are reproducible, but not necessarily close to the true value!

Multiple Choice

Which of the following data sets represents a precise, but not accurate measurement if the ACTUAL VALUE is 7:

• 7, 7, 7

• 4, 4, 4

• 4, 7, 9

• 12, 27, 15

Scientific Notation

• An easier way to express really large or really small numbers.

• To express a really larger number like 345,000,000 you move the decimal place to the LEFT until the number in front of the decimal point is between 1-10. 345,000,000. = 3.45 x 10⁸

• The number in the superscript is positive for large numbers and the superscript number represents the number of decimal places that the decimal point has moved.

Multiple Choice

What is the correct scientific notation for 65,000,000?

• 65 x 10³

• 6.5 x 10^-7

• 6.5 x 10⁷

• 65 x 10⁶

Scientific Notation

• An easier way to express really large or really small numbers.

• To express a really small number like 0.000000000123 you move the decimal place to the RIGHT until the number in front of the decimal point is between 1-10. 0.000000000123 = 1.23 x 10^-10

• The number in the superscript is negative for small numbers and the superscript number represents the number of decimal places that the decimal point has moved.

Multiple Choice

Write 3.45 x 10^-3 in standard form:

• 3,450

• 0.000345

• 0.00345

• 345,000

Multiple Choice

Write 6.78 x 10⁵ in standard form:

• 0.00000678

• 678,000,000

• 0.0000678

• 678,000

Measurement Limitations

• ALL measurements have error in them!

• A measurement consists of all known digits that can be known accurately PLUS one digit that is estimated.

• The estimated digit is always at the end of the number in a measurement.

• All of the digits that are known in a measurement are significant figures. Fewer significant figures = more rounding in a measurement = more error.

Significant Figures

Multiple Choice

Rule #1 "All NON-ZERO numbers are significant" How many significant digits in 240,000?

• 6

• 3

• 2

• No digits are significant.

Multiple Choice

Rule #2 "All zeros between non-zero numbers are significant" How many significant digits in 33,004,000?

• 5

• 7

• 8

• 3

Multiple Choice

Rule #3 "Zeros to the right of non-zero numbers are not significant unless a decimal place is used" How many significant digits in 3400?

• 4

• 2

• 3

• zero

Multiple Choice

Rule #3 "Zeros to the right of non-zero numbers are not significant unless a decimal place is used" How many significant digits in 3400.?

• 4

• 2

• 5

• 3

Multiple Choice

Rule #4 "Zeros to the left of non-zero numbers are not significant" How many significant digits in 0.0000024

• 3

• Zero

• 10

• 2

Multiple Choice

Bonus: How many significant digits in 0.000002004

• 10

• 2

• 4

• None of the above