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# Solving Problems

Reference > Science > Significant Figures

This section consists primarily of word problems, which require you to do combinations of operations using significant figures. To start off, we'll give an example, and then we'll leave it to the reader to solve the problems given in the questions section of the page!

Sample Problem

A farmer has a garden which is 20.5 meters by 8.5 meters. He also has a tarp which is 5.50 meters by 10.00 meters. If he lays the tarp over part of his garden, how much of the garden remains uncovered?

Solution

First we calculate the area of the garden: 20.5 x 8.5 = 174.25 square meters. Since one of our measurements only has two significant digits (8.5 meters) we must round this after two place values: 170 square meters.

Now we calculate the area of the tarp: 5.50 x 10.00 = 55 square meters. One of our measurements has only three significant figures, so we must write our answer as 55.0 square meters, so it will also have three significant digits.

Having found the two areas, we must subtract the tarp area from the garden area:

170 - 55.0 = 115 square meters. But now we need to use our addition/subtraction rule for significant figures. The least precise measurement is 170, which has its last significant digit in the tens place. Therefore, we must round our answer to the tens place: 120 square meters.

Scroll down to the questions section to try some word problems on your own.

## Questions

1.
One rectangular field has dimensions 52 meters by 25 meters. Another field has dimensions 75 meters by 25 meters. How much fencing is needed to go around both fields?
2.
A sphere has a radius of 3.05 meters. Another sphere has a radius of 0.95 meters. What is the sum of their volumes?
3.
Two rectangular gardens have dimensions 22 feet by 32 feet and 25.5 feet by 21.0 feet. What is the sum of the areas of the gardens?
4.
A rectangular prism has dimensions 42.5" x 13" x 125". If the prism is 1/20th filled with water, what is the water volume?
5.
The kinetic energy of an object is given as E =
1
2
mv2. If an object's mass is 2215 kg, and its velocity is 45 m/s, calculate its kinetic energy.
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Multiplying and Dividing
A Note on Rounding

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