What is Approximation?
In everyday life, exact numbers are not always necessary — and sometimes they are not even available. When a news report says a stadium held "about 20,000 fans," or a scientist describes a distance as "roughly 150 million kilometres," they are using approximation.
An approximation is a value that is close to, but not exactly equal to, the true value. We use approximations when exact values are unnecessary, impractical, or unknown.
We use the symbol ≈ to mean "approximately equal to".
For example: (rounded to the nearest hundred)
Think about estimating how many sweets are in a jar. You don't count every single one — you make a quick approximation based on what you can see. That's exactly what mathematicians and scientists do with large or complicated numbers.
Approximation is useful when:
- You need a quick estimate without a calculator
- You want to check whether a calculated answer seems reasonable
- You are working with measurements that have limited precision
- You need to communicate a number in a simpler, more memorable way
Rounding to a Place Value
The most basic form of approximation is rounding to a place value — such as the nearest 10, 100, 1000, and so on.
The Rounding Rule:
- Look at the digit immediately to the right of the place you are rounding to.
- If that digit is 0, 1, 2, 3, or 4 → round down (keep the digit the same)
- If that digit is 5, 6, 7, 8, or 9 → round up (increase the digit by 1)
Round 6,384 to the nearest hundred.
Step 1: Identify the hundreds digit → 3 (in 6,384)
Step 2: Look at the digit to its right → 8
Step 3: Since 8 ≥ 5, round up.
Round 6,724 to the nearest thousand.
Step 1: Identify the thousands digit → 6 (in 6,724)
Step 2: Look at the digit to its right → 7
Step 3: Since 7 ≥ 5, round up.
When a number is exactly halfway (e.g. 450 between 400 and 500), we always round up by convention. So to the nearest hundred.
A common mistake is rounding the wrong digit. Always identify the target place value first, then look one place to the right of it — not left!
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