3.10: Decimal Comparison
Remember Julie and the ice cream stand? Well, right after she answered the customer's question in the last Concept, another customer came up with a new questions.
A second customer came in and wanted to know if the Small cone was larger than a Big Kid cone.
Here is the chart of cone sizes.
Big Kid cone = 2.25 inches
Small cone = 2.5 inches
Julie went to see Mr. Harris for help, but he just chuckled. “It is time to brush up on your measurement and decimals my dear,” he said smiling.
Julie is puzzled and frustrated. Would you know what to say to the customers?
Pay attention and this Concept will teach you all that you need to know.
Guidance
We just finished comparing metric lengths. All of the work that we did was with whole units of measurement. We compared which ones were greater than, less than or equal to. What if we had been working with decimals?
How can we compare decimals?
When we compare decimals, we are trying to figure out which part of a whole is greater. To do this, we need to think about the number one.
1 is a whole. All decimals are part of one.
The closer a decimal is to one, the larger the decimal is.
How can we figure out how close a decimal is to one?
This is a bit tricky, but if we look at the numbers and use place value we can figure it out.
.45 ______ .67
Here we have two decimals that both have the same number of digits in them. It is easy to compare decimals that have the same number of digits in them. Now we can look at the numbers without the decimal point. Is 45 or 67 greater? 67 is greater. We can say that sixty-seven hundredths is closer to one than forty-five hundredths. This makes sense logically if you think about it.
Our answer is .45 < .67.
Steps for Comparing Decimals
- If the decimals you are comparing have the same number of digits in them, think about the value of the number without the decimal point.
- The larger the number, the closer it is to one.
What do we do if the decimals we are comparing don’t have the same number of digits?
.567 ______ .64
Wow, this one can be confusing. Five hundred and sixty-seven thousandths seems greater. After all it is thousandths. The tricky part is that thousandths are smaller than hundredths.
Is this true?
To test this statement let’s look at a hundreds grid and a thousands grid.
Now it is easier to compare. You can see that .64 is larger than .567.
How can we compare without using a grid?
Sometimes, we don’t have a grid to look at, what then?
We can add zeros to make sure that digit numbers are equal. Then we can compare.
.567 ______ .640
That made comparing very simple. 640 is larger than 567.
Our answer is that .567 < .640.
What about a decimal and a whole number?
3.4 ______ 3.56
First, we add in our zeros.
3.40 ______ 3.56
The whole number, 3 is the same, so we can look at the decimal. 40 is less than 56 so we can use our symbols to compare.
Our answer is 3.4 < 3.56.
Now that we know how to compare decimals, we can order them. Ordering means that we list a series of decimals according to size. We can write them from least to greatest or greatest to least.
.45, .32, .76
To write these decimals in order from least to greatest, we can start by comparing them. The greater a decimal is the closer it is to one whole. The smaller a decimal is the further it is from one whole. Just like when we compared decimals previously, the first thing we need to look at is the digit number in each decimal. These each have two digits in them, so we can compare them right away. Next, we can look at each number without the decimal and write them in order from the smallest to the greatest.
.32, .45, .76
32 is smaller than 45, 45 is greater than 32 but smaller than 76, 76 is the largest number
Our answer is .32, .45, .76
Now let's practice by comparing these decimals.
Example A
.0987 ______ .987
Solution: <
Example B
.453 ______ .045
Solution: >
Example C
.67 ______ .6700
Solution: =
Now back to Julie and the ice cream cones. Have you figured out how to help her?
A second customer came in and wanted to know if the Small cone was larger than a Big Kid cone. Again, Julie didn’t know what to say.
Here is the chart of cone sizes.
Big Kid cone = 2.25 inches
Small cone = 2.5 inches
Julie went to see Mr. Harris for help, but he just chuckled. “It is time to brush up on your measurement and decimals my dear,” he said smiling.
The second customer wanted to know whether the Big Kid Cone was larger or smaller than the Small cone. These cones have measurements in decimals, so we need to compare the decimals.
Big Kid cone = 2.25
Small cone = 2.5
The whole number is the same, 2, so we can compare the decimal parts.
.25 and .50
.25 < .50
2.25 < 2.5
The Big Kid cone is smaller than the Small cone.
Julie is relieved. She now understands comparing decimals and measurement. Next time, she will be ready to answer any of the customer’s questions.
Vocabulary
Here are the vocabulary words in this Concept.
- Equivalent
- means equal
- Comparing
- using greater than, less than or equal to so that we can compare numbers
- Decimals
- a part of a whole represented by a number to the right of a decimal point
- Order
- writing numbers from least to greatest or greatest to least
Guided Practice
Here is one for you to try on your own.
Write these in order from greatest to least:
.45, .678, .23
Answer
Here we have two decimals with two digits and one decimal with three. We are going to need to create the same number of digits in all three decimals.
We can do this by adding zeros.
.450, .678, .230
Now we can write them in order from greatest to least.
Our answer is .23, .45, .678.
Video Review
Here are a few videos for review.
James Sousa, Example of Ordering Decimals from Least to Greatest
James Sousa, A Second Example of Ordering Decimals from Least to Greatest
Practice
Directions: Compare the following decimals using <, >, or =
1. .4 ______ .2
2. .67 ______ .75
3. .90 ______ .9
4. .234 ______ .54
5. .123 ______ .87
6. .954 ______ .876
7. .32 ______ .032
8. .8310 ______ .0009
9. .9876 ______ .0129
10. .8761 ______ .9992
Directions: Order the following decimals from least to greatest.
11. .8, .9. .2,. 4
12. .02, .03, .07, .05, .04
13. .34, .21, .05, .55
14. .07, .7, .007, .0007
15. .87, 1.0, .43, .032, .5
16. .067, .055, .023, .011, .042
17. .55, .22, .022, .033, .055
18. .327, .222, .0222, .321, .4
19. .65, .6, .67, .678, .69
20. .45, .045, 4.5, .0045, .00045
Comparing
To determine whether a quantity is greater than, less than, or equal to another quantity.Decimal
In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Equivalent
Equivalent means equal in value or meaning.Order
Writing numbers in order commonly refers to writing them from least to greatest or greatest to least.Image Attributions
Here you'll learn how to compare and order decimals.
Concept Nodes:
Comparing
To determine whether a quantity is greater than, less than, or equal to another quantity.Decimal
In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Equivalent
Equivalent means equal in value or meaning.Order
Writing numbers in order commonly refers to writing them from least to greatest or greatest to least.