Rounding and Estimation

Rounding & estimation are very important skills both in math and in everyday life. Rounding comes as a very handy tool in the world of business when they work with amounts.

When people are in meetings, they may not want to have to worry about exact values, like 97. To make the talks easier, everybody agrees to round the number 97 up to one hundred.

It is much easier to deal with values when they are rounded to the nearest 10, 100, and so on. In mathematics, estimation is used to provide an idea about a possible answer without having to do lots of work.

While solving the full problems, estimations will tell you if you’re on track. In our daily lives, estimations will provide intelligent guesses on possible amounts and outcomes.

Suppose you’re seeing a pile of toy boxes and your estimate is that there will be some 2,500 toys. Now, it’s fine if there are actually 2,479 toys. In fact, your estimate was close enough to give a quick idea of the number of toys.

Rounding Basic Principles
In mathematics, you can be rounding up or rounding down.

We round up when we’re having a value which is half or greater of an amount that we’re rounding. So let’s say we want to be rounding to the nearest ten.

Now, when we’re given the value 26, we would be rounding up since 6 is greater than 5 (five) which is half of 10 (ten).

1. Which one will provide the closest estimate for

\(19.01 \cdot 6.05\)

Question 1 of 3

2. Round the numbers to the nearest whole ten.
\(724\; \) is approximately ____.

Question 2 of 3

3. James travels \(3,247\; m\) to the park, then \(582\; m\) to the store. He then travels \(1,634\; m\) back to his house.

Find the total distance traveled by first rounding each number to the nearest ten.

Question 3 of 3


Next Lesson: Parenthesis

Now, if we had 25, we would also be rounding up because rounding down only happens when we have a value is less than 5 (half).

When we use these same examples, when we have the number 24, we would be rounding down since 4 (four) is less than 5 (five).

And even if we were given, for example, the wacky number with decimal 24.9999, we would still be rounding down since 4.9999 is less than 5 (five).
Let’s look at a few more examples:

Round the number 34 to the nearest 10: 30
Round the number 678 to the nearest 10: 680

This works also for hundreds & thousands.

Round the number 494 to the nearest 100: 500
Round the number 627 to the nearest 100: 600
Round the number 5,872 to the nearest 1,000: 6,000
Round the number 8,452 to the nearest 1,000: 8,000

Estimations Basic Principles
The process of estimation is based on rounding numbers. In math, estimation is frequently used when we’re dealing with arithmetic including long numbers. When we would have the problem 567 + 248 while needing only a close answer, we would use estimation.

Our example could have us changing the given values to 600 plus 200, or 570 plus 250. our first step would be rounding both numbers (oo a certain place) and then do our math. Our answer then would be an estimated actual answer.

We need to keep in mind that estimation may give us answers that are pretty different from actual answers. In our example, we have estimations of 800 and 820. While the actual answer is 815, we can see that our estimations were actually somewhat off. Let’s look at 2 more interesting examples:

237 plus 469 equals…
When we round to the nearest 10 we get: 240 + 470 = 710
When we round to the nearest 100 we get: 200 + 500 = 700
The actual answer is: 706

864 minus 202 equals…
When we round to the nearest 10 we ger: 860 – 200 = 660
When we round to the nearest 100 we get: 900 – 200 = 700
The actual answer is: 662

In our first example, we got pretty close in both tries. In our second example, we can see how far off we actually got from our actual answer. You know that 700 is pretty far off the actual answer, 662.


Last Updated on November 24, 2020.

Check also