1. Place Value: Comparing, Ordering, & Rounding
for Dixon Elementary School’s
5th-Grade Math Classes

2. Comparing Numbers
When we COMPARE two UNEQUAL (not equal) numbers, we write them as an INEQUALITY.
An INEQUALITY is a relationship between 2 numbers or expressions that are not equal.
The symbols we use to write inequalities are:
< (less than), > (greater than), and
≠ (not equal to)

3. Comparing Numbers Here are some simple examples:
4 ≠ 8: 4 is NOT EQUAL TO 8
8 ≠ 4: 8 is NOT EQUAL TO 4
4 < 8: 4 is LESS THAN 8
8 > 4: 8 is GREATER THAN 4
Remember that the < or > symbols always POINT TO the number that is LESS THAN.

4. Comparing Numbers Let’s practice! What does each inequality mean?
1) a > b
2) d < e
3) g ≠ h
How do we write each inequality?
4) m is less than n
5) x is not equal to y

5. What numbers would make each expression true?
Comparing Numbers
ANSWERS:
What does each inequality mean?
1) a > b a is greater than b
2) d < e d is less than e
3) g ≠ h g is not equal to h
How do we write each inequality?
4) m is less than n m < n
5) x is not equal to y x ≠ y
What numbers would make each expression true?

6. Comparing Numbers
To compare whole numbers, we should FIRST count the digits in the 2 numbers we are comparing.
A number with more digits will always be greater than a number with fewer digits.
For example: 22,222 > 2,222 because there are 5 digits in 22,222 and only 4 digits in 2,222.

7. Comparing Numbers
If there are the same number of digits in each number, we can use our knowledge of place value to help us.

8. Comparing Numbers 86,743 Let’s compare these numbers:
86,734 and 86,743
We can stack them to make it easier to compare their place values:
86,734
86,743
Now we will compare the values of each place until we find a place that has unequal values.

9. Comparing Numbers
8 6 , 7 3 4
8 6 , 7 4 3
Once we find a place with unequal values, we compare those values.
The greater value in that first unequal place makes its entire number greater, and we can stop comparing.
YES!
Let’s move on!
Are the values equal?

10. Comparing Numbers
8 6 , 7 3 4
8 6 , 7 4 3
Because 4 tens are greater than 3 tens, the number, 86,743 > 86,734.

11. Comparing Numbers Let’s practice!
Compare the numbers, and write them as an inequality.
123,743 ≠ 98,965
73,849 ≠ 73,932
2,348,975 ≠ 2,346,992
4) 670,045 ≠ 670,046

12. Comparing Numbers ANSWERS:
Compare the numbers, and write them as an inequality.
123,743 > 98,965
73,849 < 73,932
2,348,975 > 2,346,992
4) 670,045 < 670,046

13. Ordering Numbers We COMPARE when there are only 2 numbers.
When we want to compare more than 2 numbers, we ORDER them instead.
Numbers can be ORDERED in 2 different ways:
1) greatest to least or
2) least to greatest.
It is important to read carefully to decide which we should do.

14. Ordering Numbers
When ordering GREATEST to LEAST, we list the numbers starting with the number with the GREATEST value and ending with the number with the LEAST value: 8, 4, 2.
When ordering LEAST to GREATEST, we list the numbers starting with the number with the LEAST value and ending with the number with the GREATEST value: 2, 4, 8.

15. Ordering Numbers
Just like we did with comparing numbers, we should first count the number of digits in each number.
Numbers with fewer digits are LESS THAN numbers with more digits.
After checking the number of digits, ordering numbers can be done just like comparing.

16. Ordering Numbers Let’s order these numbers LEAST to GREATEST:
, , ,714
We’ll start by stacking them, being careful to line up the places:
7 1 4
7, 4 7 1
7 4 1
7, 4 1 7
7 0, 7 1 4

17. Ordering Numbers
7 1 4
7, 4 7 1
7 4 1
7, 4 1 7
7 0, 7 1 4
Now let’s count digits.
The 3-digit numbers < 4-digit numbers, and the 4-digit numbers < 5-digit number.
3 digits
4 digits
5 digits

18. Ordering Numbers
Since we’re ordering LEAST to GREATEST, we’ll start by comparing the 3-digit numbers since they’re less than the others.
7 1 4
7, 4 7 1
7 4 1
7, 4 1 7
7 0, 7 1 4
714 < 741
3 digits

19. Ordering Numbers So our list starts: 714 < 741.
Now let’s do the same with the 4-digit numbers.
7 1 4
7, 4 7 1
7 4 1
7, 4 1 7
7 0, 7 1 4
7,471 > 7,417
4 digits

20. Ordering Numbers The next 2 in our list are: 7,417 < 7,471.
714 < 741 < 7,417 < 7,471
Finally, we know the 5-digit number is the greatest because it has more digits than the others, so it will finish our least-to-greatest list:
714 < 741 < 7,417 < 7,471 < 70,714

21. Ordering Numbers
If we are ordering a group with the same number of digits, we will just stack them and compare by place value:
6, , , , ,590
Let’s order the numbers above, greatest to least.

22. Ordering Numbers
We’ll stack them first, lining up each place.
6, 5 9 9
6, 6 0 0
6, 5 0 9
6, 6 0 6
6, 5 9 0
The numbers in the greatest place, the one thousands place, are the same, so we will move to the hundreds place.

23. Ordering Numbers
6, 5 9 9
6, 6 0 0
6, 5 0 9
6, 6 0 6
6, 5 9 0
The numbers in the hundreds place are not equal, so we’ll look at the largest values, 600.
Both of those numbers are followed by 0s, so we have to look at the ones place.
6 ones > 0 ones, so 6,606 is greatest.

24. Ordering Numbers
Our list will begin: 6,606 > 6,600.
Now, we’ll compare the numbers with 5s in the hundreds place.
6, 5 9 9
6, 6 0 0
6, 5 0 9
6, 6 0 6
6, 5 9 0
Two of the numbers have 9s in the tens place.
So we have to move to the ones place.

25. Ordering Numbers
When we compare the numbers with 5s in the hundreds place, we get:
6,599 > 6,590 > 6,509
So, the final order, greatest to least, is:
6,606 > 6,600 > 6,599 > 6,590 > 6,509

26. Ordering Numbers Let’s practice!
Order these numbers, least to greatest:
8, , , , ,948
Order these numbers, greatest to least:
65, , , , ,621

27. Ordering Numbers ANSWERS: Order these numbers, least to greatest:
8, , , , ,948
8,944 < 8,946 < 8,948 < 8,962 < 8,964
Order these numbers, greatest to least:
65, , , , ,621
66,621 > 66,001 > 65,612 > 65,602 > 65,598

28. Rounding Numbers We round numbers to estimate computations.
When we round, we make numbers easier to work with and keep their values close to their original value.
Numbers are rounded to specific places.
The value of a rounded number can change based on the place to which it is rounded.

29. Rounding Numbers Let’s look at this number: 7,619.
When rounded to the thousands place, the value is 8,000.
When rounded to the hundreds place, the value is 7,600.
When rounded to the tens place, the value is 7,620.

30. Round 18,392 to the nearest thousand.
Rounding Numbers
Here’s how it’s done…
Round 18,392 to the nearest thousand.
Step 1: Underline the place we’re rounding to: 18,392 (thousands place).
Step 2: Look at the place to its right: 18,392
Step 3: If the digit is 4 or less, the underlined digit stays the same; if the digit is 5 or more, the underlined digit rounds up to the next number.

31. Rounding Numbers 18,392 Since 3 is less than 4, the 8 stays the same.
After deciding whether a number stays the same or rounds up, the numbers before the underlined digit remain the same, and the numbers behind the underlined digit become 0s: 18,000.
So 18,392 rounded to the nearest thousand is 18,000.

32. Rounding Numbers
Let’s round the same number to the nearest 100: 18,392
What do we do first?
Underline the place we’re rounding to!
18,392
Now what?
Look at the number to its right!
Next?
Is it 4 or less or 5 or more?

33. Round the underlined digit up to 4!
Rounding Numbers
18,392
Since 9 is “5 or more,” what do we do?
Round the underlined digit up to 4!
And then?
Leave the numbers before the underlined digit (18) the same, and change the numbers behind it (92) to 0s!
So what does 18,392 become when rounded to the nearest hundred?
18,400!

34. Rounding Numbers Let’s practice!
Round each number to the underlined place.
64,892
243,837
3,099

35. Rounding Numbers ANSWERS: Round each number to the underlined place.
64,892 = 65,000
243,837 = 243,800
3,099 = 3,100

36. Pop Quiz! Compare and write as an inequality. 76,045 ≠ 76,050
426,099 ≠ 425,100
649,769 ≠ 649,796
Order greatest to least.
4) 2, , , ,401
Round to the underlined place.
5) 632,196
6) 808,495

37. Pop Quiz ANSWERS! Compare and write as an inequality.
76,045 < 76,050
426,099 > 425,100
649,769 < 649,796
Order greatest to least.
4) 2, , , ,401
2,401 > 2,359 > 2,354 > 2,345
Round to the underlined place.
5) 632,196 = 632,200
6) 808,495 = 808,000