Approximation is the act of creating or determining a value that is not perfect, but just good enough to be useful for your situation. I do this all the time when I go to the hardware store to purchase lumber in the form of rectangular boards. Lumber comes in fixed lengths that usually broken up in intervals of 2 feet up to 12 feet long, at least in the hardware stores I have been to. If I know I need a board to be 9 feet 4 inches long, I would make a quick approximation that I will need a 10 foot board. 8 feet would be too short and the 12-foot version would result in wasted material and money on my part. These worksheets and lessons help students understand how to identify a value that is acceptably close to an expected value.
Aligned Standard: HSN-Q.A.3
- Lots of Approximating Lesson- Take a single value and rewrite based on hundreds place, significant figures, and decimal places.
- Matching Sheet- Some values might be able to cross over, but in order for every problem to be correct you need decisive choices.
- Approximating All Kinds of Values Worksheet 1 - You are given a decimal value and asked to approximate it in sig figs, basic place value, and whole numbers.
- Approximating Powers of Ten - Watch that decimal point just bounce around everywhere.
- Approximating Decimals - More fun with decimals for you.
- Answer Keys - These are for all the unlocked materials above.
More Practice Versions
One for each of the basic approaches to renaming numbers.
- Powers of Ten Worksheet 2 - Identify the place value that is needed for each case.
- Decimals Worksheet 2 - Round to off each number from one to four.
- Significant Figures Worksheet 1 - We are asked to rewrite the value in 1-4 significant figures.
- Significant Figures Worksheet 2 - The more practice you can have, the better.
All Kinds of Practice Worksheets
These sheets cover all major forms that students will encounter until they reach trigonometry.
- Approximate Marathon Worksheet 2 - Read the column headings carefully. This is a mixed exercise.
- Worksheet 3 - More work to get it right.
- Worksheet 4 - We would look at the integer in the tens place to tell us if we round up or down.
How Do You Go About Approximating a Value?
Approximation takes a crucial place in mathematics. Approximating a value is the act or a process of finding/calculating a value that is considered acceptable or close enough to an exact value. This value is then called approximate value, and the act/process is called approximation. In scientific experiments and engineering, approximation has always played a key role because it is always almost impossible to find the exact answer to a certain value under certain conditions. In many business situations doing this with financial calculations can increase the speed at which decisions are made. Which can in turn lead to an elevated rate of progress and production.
There is always a need to approximate values in circumstances where it is near impossible to make accurate measurements and also we do this because certain numbers are difficult to express in decimal notation. For such cases, approximations are used. For example, if you have to approximate decimal or irrational numbers, such as pi that is a nonterminating or nonrepeating decimal, the number 3.1415926 can be approximated to 3.14 or 3.1416 and so on until the desired accuracy is reached.
The method of approximation is not merely limited to problems or simple numbers. It is also used for complex mathematical concepts. These are widely used in graphs and calculating the value of a function also. It is often used in theoretical models where there is nothing to measure or areas where the information is just not complete. Without approximation they would not be able to render a helpful model or representation of what ever phenomena they are studying.
We often use approximation in our daily routine and do not even realize it. For example, if some one asked you how long your ride to school was, it may be exact 22 minutes, but you will most likely respond with 20 or 25 minutes. In most cases just because it sounds better for your audience and that simple rounding procedure made them feel more comfortable. An entire industry is built around using approximation. Sneaker and show sizes are all about this process. Do you think that everyone on the planet has 1 of 15 different shoe sizes or only 4 different widths of their feet?
How you go about approximating a value differs entirely based on the circumstance. In some instances, it is a simple exercise in either rounding up or down to the highest place value. In other cases, it is rounding to an exact place value within your value. It all depends on you situation and how accurate you need to be. You must first determine that level before you can proceed.