Estimating And Comparing and Ordering

Decimals

Lesson 1-3 & 1-4

RoundingIdentify the place you are rounding to, and place a box around it.

Check the digit to the right. If it is greater than or equal to 5, then the number in the box increases by one. If it is less than 5, then the number in the box stays the same.

Keep everything before the box. Everything after the box becomes zero. If the zeroes come at the end of a decimal, they can be dropped.

Example: Round 4,525 to the nearest hundreds place.

4,525 __ , __ __ __54 0 0

Example 2: Round 13.56 to the nearest tenths place.

13.56 __ __ . __ __61 3 0

13.6 is the answer.

Estimating the Nearest Whole Number

Most of the time, you will be asked to round to the nearest whole number.

Round to the ones place, and drop the decimal part of your number.

Example: Estimate the sum of 10.93 and 3.25.

10.93+ 3.25

11+ 314

Compatible Numbers

Compatible numbers are numbers that are easy to compute mentally.

Change your numbers to compatible numbers that are close to the original numbers.

For example, instead of multiplying 5.21 by 78.03, it’s easier to think about multiplying 5 times 80.

When we estimate, we can say that the product of 5.21 and 78.03 is about 400.

Front-End Estimation

Add the “front-end” digits, ignoring the decimals.

Estimate the decimals.

Add the estimated decimal to the front-end sum.

Example5.45

9.89

3.53

6.03+

Front-end: 5 + 9 + 3 + 6 = 23

Decimals:

•.89 is close to 1.

•.03 is close to 0.

•.45 + .53 is close to 1.

•1 + 0 + 1 = 2

Put the front-end with the decimal: 23 + 2 = 25.

About 25

Front-End Estimation

Comparing and Ordering Decimals

Using ModelsIf you are comparing tenths to hundredths, you can use a tenths grid and a hundredths grid. Here, you can see that 0.4 is greater than 0.36.

Using a Number Line

Determine the highest and lowest number, and then draw tenths. If hundredths are necessary, draw those.Example: Put the following numbers in order on the number line: 1.4; 1.65; 1.58; 1.84; 1.8In this example, the number line must be between 1.4 and 1.84.

First, fill in the tenths.

1.5 1.6 1.7

Then, fill in the hundredths.

Place the decimals on the line.

1.41.651.58 1.841.8

Now the decimals are in order.

The Easy Way

Line up the numbers vertically by the decimal point.

Add “0” to fill in any missing spaces.

Compare from left to right.

Put these numbers in order:

12.5; 12.24; 11.96; 12.3612 . 512 . 2411 . 96

12 . 36

Fill in the missing space with a zero.

11.96 < 12.24 < 12.36 < 12.5

0

Homework Timep. 16, #2-22 evens and p.21, #6-20 evens

The above image is Michigan in the fall provided by jacalynsnana

Classwork TimePlay this Math Baseball Game to help you Round Decimals

Review the Rules for Comparing and Ordering Decimals and then play the game!

Need more practice? Go to AAA Math to Compare and Order Decimals