Unit 0 Lesson 2 Check for Understanding
Measuring With Significant Digits
Introduction
All scientific conclusions are based on measurements and observations. In the case of quantitative measurements, scientists try to be as accurate as possible. Accuracy is the closeness of a measurement to its true or actual value.
Volume
Volume is measured with graduated cylinders. When a liquid is poured inside, it forms a meniscus, or a curve at the top of the liquid. There are two important rules in reading a meniscus accurately:
-
Measurements must be taken from the bottom of the meniscus.
-
You must look at the meniscus from eye level.
Length
Length is measured with a ruler or meter stick. In this class, the numbered lines will represent centimeters, while the smaller
un-numbered lines are millimeters.
Precision & Significant Figures
The precision of a measurement is determined by the calibration of the instrument you are using (the smallest division on the measuring scale). In a measurement, significant figures consist of the digits definitely known + one estimated digit.
In the example above, measurement A is definitely beyond the 7cm mark and the 0.8cm mark. By looking carefully, we can estimate that the measurement is halfway between 7.8cm and 7.9cm, so the final measurement is 7.85cm. This measurement has three significant digits.
-
How would you record measurement B with three significant digits? 9.21
-
Practice recording precise and accurate measurements with the three graduated cylinders shown below. Remember to measure from the bottom of the meniscus. Assume all units are milliliters (mL).
a ) 56.0
b ) 4.33
c ) 23.6
How many significant digits does each of these measurements have? 3
- Record each of the following measurements of temperature with the correct number of significant digits.
a) 68.0
b) -2.9
c) 10.9
Scientific Notation Practice
Convert the following numbers into standard scientific notation
-
45,700 - > 4.57 * 10 ^ 4
-
0.90 - > 9 * 10 ^ -1
-
24, 212, 000 - > 2.4212 * 10 ^ 7
-
0.000665 - > 6.65 * 10 ^ -4
Convert the following numbers in scientific notation into ordinary notation
-
3.825 x 10^3 - > 3825
-
6.3 x 10^4 - > 63000
-
2.3 x 10^-2 - > 0.023
-
4.44 x 10^-6 - > 0.00000444