Navigating the World of Estimation

Understanding Estimation

Estimation is like making an educated guess to get close to the answer without calculating everything exactly. It’s especially useful in math to check if an answer is reasonable or when we don’t need precise numbers.

Why Estimate?

• Speed: Estimation helps us get a quick answer.
• Accuracy Check: It’s a great way to check if our final answer makes sense.
• Real-Life Use: In everyday life, we estimate costs, distances, and even time!

Rounding for Estimation

To estimate, we often round numbers to make them easier to work with. Here’s a quick reminder of rounding:

• Round up if the checking digit (the one after the digit you’re rounding to) is 5 or higher.
• Round down if the checking digit is 4 or lower.

Example:

If we want to estimate $389 + 724$:

1. Round $389$ to $400$
2. Round $724$ to $700$
3. Add the rounded numbers: $400 + 700 = 1100$

So, the estimate for $389 + 724$ is about $1100$

 

Over-Estimates and Under-Estimates

When estimating, sometimes we round up (creating an over-estimate), and sometimes we round down (creating an under-estimate).

• Over-Estimate: This happens when we round numbers up. The estimate is higher than the actual value.
• Under-Estimate: This happens when we round numbers down. The estimate is lower than the actual value.

Knowing when your estimate might be too high or too low can be helpful in understanding how close it is to the actual answer.

Example

Estimate $59 \times 42$ by rounding each number to the nearest $10$

1. Round $59$ up to $60$ (over-estimate)
2. Round $42$ down to $40$ (under-estimate)
3. Multiply: $60 \times 40 = 2400$

Since we used both an over-estimate and an under-estimate, our estimate of 240024002400 is close to the actual answer.