Ch. 1-1 Using Estimation StrategiesAugust 23rd, 2013

How do we round numbers?

Round to the place of the underlined digit.

1. 3.528

2. 24,106

3. 54

4. 131,295

5. 449

6. 4,951

7. 229,999

8. 82,729

9. 998

Rounding Cont…

Round 3,507 to the nearest ten, nearest hundred, and nearest thousand.

Nearest ten : 3,510 Nearest hundred : 3,500 Nearest thousand : 4,000

Why do we round?

We often round numbers to estimate an answer.

What symbol do we use that means, “is approximately to”? ≈

Estimating a Sum or Difference

What is 3.27 – 0.88 approximately equal to? It would be easy for us to subtract two whole

numbers. Can we round the two numbers above to the nearest whole number and then subtract?

Now we can estimate the difference as… 3.27 – 0.88 ≈

3 – 1 ≈ 2

Estimating a product

A living room is 10.5 ft by 9.25 ft. Use rounding to estimate the room’s area in square feet.

What are we going to round to in order to make the problem easier?

Estimation: 10.5 X 9.25 ≈

11 X 9 ≈ 99

Therefore the area of the living room is about 99 ft2.

Definition

Compatible Numbers :

Are numbers that are easy to compute mentally. You can use compatible numbers to estimate.

Simply change the numbers of the problem to make the calculation easier.

(We usually use this method for finding quotients)

Compatible Numbers

Example:

7.25/3.10

Even if we round to the nearest whole number, 7/3 is still a number we can’t compute in our head easily.

So, using the definition, we can change the numbers to make the calculation easier.

6/3 = 2.

So, 7.25/3.10 ≈ 6/3 = 2.

Real life problem

Suppose I have $50.25 to buy as many movie tickets as I can. Movie tickets cost $7.95 on a Sunday afternoon. About how many tickets can I buy?

50.25 ≈ 50 7.95 ≈ 8 Do we easily know what 50/8 = ? What compatible

numbers can we change 50/8 to be? 48/6 = 6. Therefore, I can purchase approximately 8 tickets.