Name: __________________________ Class: ____________________ Date: _____________
Density Calculations with Significant Digits
Introduction
Density is a measurement of how compact a substance is. The unit of density we will use most often in
chemistry is grams/milliliter, or g/mL.
Significant Figures in Addition and Subtraction
When adding or subtracting two or more numbers, the answer should be rounded to the least number of
decimal places in your data.
Example: Add the following masses: 42.56 g + 39.460 g + 4.1 g
Solution:
42.56 g
39.460 g
4.1 g
86.120 g
+
Rounded answer = 86.1g
Complete the following problems, rounding the answer to the correct number of decimal places.
Calculator Answer
Rounded Answer
a. 14.1g + 0.54g
_______________
_______________
b. 1.001mL + 5.1mL + 10.55mL
_______________
_______________
c. 20lb - 0.5lb - 1.4lb =
_______________
_______________
Significant Figures in Multiplication and Division
When multiplying or dividing two or more numbers, the answer should be rounded to the least number of
significant figures in your data.
Example: Calculate the area of a 5.2cm x 9.80cm rectangle
Solution:
x
5.1cm
9.80cm
50.96cm2
(2 significant figures)
(3 significant figures)
Rounded answer = 51cm2 (2 significant figures)
Complete the following problems, rounding the answer to the correct number of significant figures.
Calculator Answer
Rounded Answer
a. 10.0m/s * 5.9s
_______________
_______________
b. 25cm * 25cm
_______________
_______________
c. 125m2 / 25m
_______________
_______________
Written by James Dauray
http://www.aurumscience.com
Page 1
Calculating Density
Density cannot be easily measured directly. However, it can be calculated by measuring the volume and
mass of the substance, then using the following formula:
To find the volume of a solid object, it is placed
(carefully) into a graduated cylinder containing a premeasured amount of liquid.
a. What is the volume of the rock shown to the
right? Show all calculations, and follow the
rules of measuring with significant figures.
The same rock is placed on a triple-beam balance, with the following result.
a. Record the mass using the correct number of significant digits.
b. Calculate the density of the rock using the formula at the beginning of this section. Follow the
rules for division with significant figures.
Practice Problems
Solve each of the problems below using the density equation. Show work, and follow rules for significant
figures.
1.
A 5.00 cm3 sample of gold has a mass of 96.5 g. Calculate the density of gold.
2.
You measure the mass of a large piece of wood to be 75.1g. The wood has a volume of
78.5cm3. Calculate the density of the wood.
3.
The density of table sugar is 1.59 g/cm3. What is the volume of 7.85 g of sugar?
4.
Aluminum has a density of 2.70 g/cm3. Calculate the mass of a solid piece of aluminum whose
volume is 1.50 cm3.
5.
Silver has a density of 10.5g/cm3. Aluminum has a density of 2.7g/cm3. If you have a 2cm x
2cm x 2cm cube of a silver metal that has a mass of 21.6g, is it aluminum or silver?