Approximation facts for kids
An approximation is like a close guess or a simpler version of something that isn't perfectly exact. We use approximations when we don't know the exact number, or when the exact number is too long or complicated to use. It's about being "close enough" for what you need.
For example, if you wanted to add 2.0002 and 2.0003, you could quickly add 2 and 2. This would be an approximation. Or, if you have $78.23 left, you might tell a friend you have "about $80." In mathematics, we use the 
symbol to show an approximation. For instance, 
means pi is approximately 3.1416.
Contents
What is an Approximation?
An approximation helps us deal with numbers or measurements that are very precise, unknown, or hard to work with. Instead of using the exact value, we use a simpler one that is very close. This makes calculations easier and faster.
Why Do We Use Approximations?
- When the exact value isn't known: Sometimes, it's impossible to know the exact number. For example, when measuring something, there's always a tiny bit of uncertainty.
- When the exact value is too complex: Numbers like pi (
) go on forever without repeating. It's much easier to use an approximation like 3.14 or 22/7. - For quick estimates: If you're trying to figure out roughly how much something will cost, you might round prices to the nearest dollar.
- To simplify problems: In science or engineering, complex equations can often be simplified by using approximations, especially when small details don't change the overall result much.
Examples of Approximations in Daily Life
- Rounding money: Saying "about $50" instead of $49.75.
- Estimating time: Saying "around 10 minutes" instead of 9 minutes and 47 seconds.
- Distances: Saying "about 100 miles" instead of 98.6 miles.
- Cooking: Using "a pinch" of salt instead of an exact measurement.
History of Approximations
People have used approximations for thousands of years. Ancient civilizations needed ways to measure land, build structures, and track time, often without perfect tools.
Archimedes and Pi
One famous example comes from the ancient Greek mathematician Archimedes. He lived around 287–212 BC. Archimedes wanted to find a good approximation for , which is the ratio of a circle's circumference to its diameter.
He did this by drawing polygons (shapes with straight sides) inside and outside a circle.
- He started with a polygon with a few sides.
- Then, he kept increasing the number of sides of the polygons.
- As the number of sides got larger, the polygons looked more and more like a circle.
- By calculating the perimeter of these many-sided polygons, he could get closer and closer to the true circumference of the circle.
This method allowed him to figure out that was somewhere between 3 + 10/71 and 3 + 1/7. This was a very accurate approximation for his time!
Related pages
See Also
In Spanish: Aproximación para niños
