1. Chapter 1 Chemistry and Measurements
1.5
Measured Numbers and
Significant Figures

2. Measured Numbers
Measured numbers are the numbers obtained when you measure a quantity such as your height, weight, or temperature.

3. Writing Measured Numbers
To write a measured number,
observe the numerical values of marked lines
estimate value of number between marks
the estimated number is the final number in your
measured number

4. Writing Measured Numbers for Length
The lengths of the objects are measured as
(a) 4.5 cm
(b) 4.55 cm
(c) 3.0 cm

5. A Number Is Significant When
A number is a significant figure (SF) if it is Example a. not a zero 4.5 g 2 SF b. a zero between digits 205 m 3 SF c. a zero at the end of a 50. L 2 SF decimal number d. in the coefficient of a 4.8 x 105 m 2 SF number written in scientific notation

6. A Number Is NOT Significant When
A number is not significant if it is Example a. at the beginning of a decimal number s 1 SF b. used as a placeholder in a large number without a decimal point m 2 SF

7. Learning Check
Identify the significant and nonsignificant zeros in each of the following numbers: A m B g C L

8. Solution
Identify the significant and nonsignificant zeros in each of the following numbers:
A m
The zeros preceding 2 are not significant.
The digits 2, 6, 5 are significant.
The zero in last decimal place is significant SF
B g
The zeros between nonzero digits or at the
end of decimal numbers are significant SF

9. Solution
Identify the significant and nonsignificant zeros in each of the following numbers:
C L
The zeros between nonzero digits are significant.
The zeros at end of a number with no decimal
are not significant SF

10. Exact Numbers Exact numbers are numbers obtained by counting 8 cookies
in definitions that compare two units 6 eggs
in the same measuring system 1 qt = 4 cups
1 kg = 1000 g

11. Learning Check
Identify the numbers below as measured or exact and give the number of significant figures in each measured number: A. 3 coins B. the diameter of a circle is cm C. 60 min = 1 h

12. Solution
Identify the numbers below as measured or exact and give the number of significant figures in each measured number: A. 3 coins is a counting number and therefore is an exact number. B. The diameter of a circle is cm. This is a measured number and the zero is significant, so it contains 4 SF. C. 60 min = 1 h is a definition and therefore an exact number.