Place Value and Whole Numbers
The number system we use is based on units of 10. A number like 7,825 is a
whole number . A digit and its place-value position name a number. For
example, in 7,825, the digit 7 is in the thousands place, and its value is 7,000.
Place-Value Chart
ones
tens
hundreds
thousandds
ten thousands
hundred
thousands
one million
ten millions
hundred
millions
one billion
1,000,000,000 100,000,000 10,000,000 1,000,000 100,000 10,000 1,000 100 10 1
8 2 5
Each set of three digits is called a period.
Periods are separated by a comma.
Identify Place Value
Identify the place-value position of the digit 9 in 597,240,618.
one million
hundred
thousands
ten thousands
thousandds
hundreds
tens
5
9
7
2
4
0
6
1 8
ones
ten millions
1
hundred
millions
1,000,000,000 100,000,000 10,000,000 1,000,000 100,000 10,000 1,000 100 10
one billion
Prerequisite Skills
Prerequisite Skills
The digit 9 is in the ten millions place.
Numbers written as 7,825 and 597,240,618 are written in standard form .
Numbers can also be written in word form . When writing a number in
word form, use place value. At each comma, write the name for the period.
Write a Whole Number in Word Form
Write each number in word form.
4,567,890
Standard Form
4,567,890
Word Form
four million five hundred sixty-seven thousand
eight hundred ninety
804,506
Standard Form
804,506
Word Form
eight hundred four thousand five hundred six
586 Prerequisite Skills
Numbers can also be written in expanded notation .
Prerequisite Skills
Write a Whole Number in Expanded Notation
Write 28,756 in expanded notation.
Step 1
Write the product of each digit and its place value.
20,000 (2 10,000)
8,000 (8 1,000)
700 (7 100)
50 (5 10)
6 (6 1)
Step 2
The digit 2 is in the ten thousands place.
The digit 8 is in the thousands place.
The digit 7 is in the hundreds place.
The digit 5 is in the tens place.
The digit 6 is in the ones place.
This is 28,756 written
in expanded notation.
Write the sum of the products.
28,756 (2 10,000) (8 1,000) (7 100) (5 10) (6 1)
Exercises
Identify each underlined place-value position.
1. 438
2. 6,845,085
3. 413,467
4. 3,745
5. 72,567,432
6. 904,784,126
7. Write a number that has the digit 7 in the billions place, the digit 8 in the
hundred thousands place, and the digit 4 in the tens place.
Write each number in word form.
8. 263
9. 2,013
10. 54,006
11. 47,900
12. 567,460
13. 551,002
14. 7,805,261
15. 1,125,678
16. 102,546,165
17. 582,604,072
18. 8,146,806,835
19. 67,826,657,005
Write each number in standard form.
20. forty-two
21. seven hundred fifty-one
22. three thousand four hundred twelve
23. six thousand nine hundred five
24. six hundred thousand
25. sixteen thousand fifty-two
26. seventy-six million
27. two hundred twenty-four million
28. three million four hundred thousand
29. ten billion nine hundred thousand
Write each number in expanded notation.
30. 86
31. 398
32. 620
33. 5,285
34. 4,002
35. 7,500
36. 85,430
37. 524,789
38. 8,043,967
39. PIANOS There are over ten million pianos in American homes,
businesses, and institutions. Write ten million in expanded notation.
40. BOOKS The Library of Congress in Washington, D.C., has
24,616,867 books. Write this number in word form.
Prerequisite Skills
587
Prerequisite Skills
Comparing and Ordering Whole Numbers
When comparing the values of two whole numbers, the first number is
either less than, greater than, or equal to the second number. You can use
place value or a number line to compare two whole numbers.
less than
greater than
Method 1 Use place value.
equal to
Words
• Line up the digits at the ones place.
• Starting at the left, compare the digits in each place-value
position. In the first position where the digits differ, the
number with the greater digit is the greater whole number.
Method 2 Use a number line.
• Numbers to the right are greater than numbers to the left.
• Numbers to the left are less than numbers to the right.
Compare Whole Numbers
Replace the
in 25,489
25,589 with , , or to make a true sentence.
Method 1 Use place value.
25,489
25,589
Method 2 Use a number line.
Line up the digits.
25,489
25,589
Graph and then
compare the numbers.
Compare.
The digits in the hundreds
place are not the same.
Since 4 5, 25,489 25,589.
25,400 25,500 25,600
Since 25,489 is to the left of 25,589,
25,489 25,589.
Order Whole Numbers
Order 8,989, 8,957, and 8,984 from least to greatest.
8,957 is less than both 8,989 and 8,984 since 5 8 in the tens place.
8,984 is less than 8,989 since 4 9 in the ones place.
So, the order from least to greatest is 8,957, 8,984, and 8,989.
Exercises
with or to make a true sentence.
Replace each
1. 496
489
4. 9,999
7. 75,495
10. 245,000
10,001
75,606
24,500
2. 5,602
5,699
3. 3,455
5. 8,993
8,399
6. 13,405
8. 400,590
11. 675,656
401,001
6,756,560
3,388
9. 501,222
12. 1,000,000
14,003
510,546
989,566
Order each list of whole numbers from least to greatest.
13. 678, 699, 610
14. 4,654, 4,432, 4,678
15. 42,000, 4,200, 41,898
16. STATES Alabama has a total area of 52,237 square miles. Arkansas has
an area of 53,182 square miles. Which state is larger?
588 Prerequisite Skills
Symbol
Adding and Subtracting Whole Numbers
Prerequisite Skills
To add or subtract whole numbers, add or subtract the digits in each
place-value position. Start at the ones place.
Add or Subtract Whole Numbers
Find each sum or difference.
587 162
125 203
125
203
328
587
162
425
Line up the digits
at the ones place.
Add the ones.
Line up the digits
at the ones place.
Subtract the ones.
Add the tens.
Subtract the tens.
Add the hundreds.
Subtract the hundreds.
You may need to regroup when adding and subtracting whole numbers.
Add or Subtract Whole Numbers
with Regrouping
Find each sum or difference.
612 59
387 98
5 10 12
11
387
98
485
612
59
553
Line up the digits
at the ones place.
Add the ones. Put the 5 in the
ones and place the 1 above
the tens place.
Add the tens. Put the 8 in the
tens place and the 1 above
the hundreds place.
Line up the digits
at the ones place.
Since 9 is larger than 2,
rename 2 as 12. Rename the
1 in the tens place as 10 and
the 6 in the hundreds place
as 5. Then subtract.
Add the hundreds.
Exercises
Find each sum or difference.
1.
506
30
2.
315
583
3.
1,342
627
4.
5,042
2,143
5.
71,235
27,563
6.
468
21
7.
895
472
8.
1,872
460
9.
6,056
5,052
10.
74,618
23,311
11.
2,680
945
12.
5,126
896
13.
2,973
1,689
14.
1,089
5,239
15.
16,999
25,509
16.
982
36
17.
487
199
18.
6,052
5,456
19.
64,205
3,746
20.
215,000
12,999
21. PLANETS The diameter of Earth is 7,926 miles. The diameter of Mars is 4,231 miles.
How much greater is the diameter of Earth than the diameter of Mars?
Prerequisite Skills
589
Prerequisite Skills
Multiplying Whole Numbers
To multiply a whole number by a 1-digit whole number, multiply from right
to left, regrouping as necessary.
Multiply by a 1-Digit Whole Number
Find each product.
148 9
76 8
4
76
8
608
47
8 6 48. Put the 8 in
the ones place. Put the 4
above the tens place.
148
9
1,332
8 70 560, and 560 40 600.
9 8 72. Put the 2 in the ones
place. Put the 7 above the tens place.
9 40 360, and 360 70 430.
Put the 3 in the tens place. Put the 4
above the hundreds place.
9 100 900, and 900 400 1,300.
When you multiply by a number with two or more digits, write individual
products and then add.
Multiply by a 2-Digit Whole Number
Find each product.
84 65
535 24
84
65
420
5040
5460
535
24
2,140
10,700
12,840
Multiply. 84 5 420
Multiply. 84 60 5,040
Add. 420 5,040 5,460
Multiply. 535 4 2,140
Multiply. 535 20 10,700
Add. 2,140 10,700 12,840
Exercises
Find each product.
1.
40
5
2.
23
3
3.
81
6
4. 172
5.
3
361
7
6. 721
7. 513
8. 634
9. 2,821
10. 5,045
4
3
2
4
2
11.
28
10
12.
52
20
13.
75
19
14.
54
27
15.
414
22
16.
321
34
17.
522
32
18.
613
24
19.
525
150
20.
678
123
21. FOOD The average person in the U.S. eats about 36 pounds of frozen
food per year. How many pounds would an average family of four eat?
590 Prerequisite Skills
Dividing Whole Numbers
Prerequisite Skills
When dividing whole numbers, divide in each place-value position from
left to right. Recall that in the statement 50 2 25, 50 is the dividend ,
2 is the divisor , and 25 is the quotient .
Divide Whole Numbers
Find each quotient.
342 9
6,493 78
38
9342
27
72
72
0
83 R19
786493
624
253
234
Divide in each place-value
position from left to right.
Since 72 72 0,
there is no remainder.
19
Divide in each place-value
position from left to right.
Since 253 234 19,
the remainder is 19.
Exercises
Find each quotient.
1. 37
2
2. 49
6
3. 28
4
4. 69
18
5. 89
76
6. 79
03
7. 126
0
8. 257
5
9. 159
0
10. 342
04
11. 271
35
12. 534
24
13. 242
40
14. 255
00
15. 156
00
16. 63
84
17. 346
12
18. 487
20
19. 311
,9
53
20. 471
,9
27
21. 191
,0
45
22. 183
,6
72
23. 329
,8
24
24. 278
,1
54
25. 89
1
26. 59
9
27. 68
0
28. 86
85
29. 42
73
30. 53
87
31. 127
5
32. 189
9
33. 275
6
34. 338
5
35. 239
7
36. 292
10
37. 624
39
38. 372
99
39. 161
34
40. 534
83
41. 501
2,5
75
42. 492
9,6
70
43. 323
8,6
93
44. 469
2,3
30
45. 268
0,3
11
46. 1007
06
47. 1008
42
48. 2009
00
49. 5007
05
50. 3006
02
51. 4001
,6
32
52. 6008
,4
07
53. MONEY In 2000, there were $3,440,000 in $10,000 bills in circulation
in the U.S. How many $10,000 bills were there?
54. MEASUREMENT One acre is the same as 43,560 square feet. It is
also equal to 4,840 square yards. How many square feet are there in
one square yard?
Prerequisite Skills
591
Prerequisite Skills
Estimating with Whole Numbers
When an exact answer to a math problem is not needed, or when you want
to check the reasonableness of an answer, you can use estimation . There
are several methods of estimation. One common method is rounding .
To round a whole number, look at the digit to the right of the place being
rounded.
• If the digit is 4 or less, the underlined digit remains the same.
• If the digit is 5 or greater, add 1 to the underlined digit.
Estimate by Rounding
Estimate by rounding.
478 12
30,798 4,115 1,891
30,798
4,115
1,891
31,000
4,000
2,000
37,000
In this case,
each number
is rounded to
the same
place value.
So, the sum is about 37,000.
478
12
500
10
5,000
In this case,
each number
is rounded to
its greatest
place value.
So, the product is about 5,000.
Clustering can be used to estimate sums if all of the numbers are close to
a certain number.
Estimate by Clustering
Estimate by clustering.
97 102 99 104 101 98
748 751 753 747
All of the numbers are clustered
around 100. There are 6 numbers.
So, the sum is about 6 100
or 600.
All of the numbers are clustered
around 750. There are 4 numbers.
So, the sum is about 4 750
or 3,000.
Compatible numbers are two numbers that are easy to compute mentally.
Estimate by Using Compatible Numbers
Estimate by using compatible numbers.
102 24
24102
4
25100
So, the quotient is about 4.
71 19 28 83
71 19 28 83
(70 30) (20 80)
100 100 or 200
The sum is about 200.
592 Prerequisite Skills
70 20 30 80
Prerequisite Skills
Another strategy that works well for some addition and subtraction
problems is front-end estimation . In this strategy, you first add or subtract
the left-most column of digits. Then, add or subtract the next column.
Use Front-End Estimation
Estimate by using front-end estimation.
3,542 1,280
739 259
739
259
900
739
259
980
3,542
1,280
2,000
Add the leftmost column.
Subtract the leftmost column.
3,542
1,280
2,300
Add the next digits.
Annex a zero.
Subtract the next digits.
Annex two zeros.
So, the difference is about 2,300.
So, the sum is about 980.
Exercises
Estimate by rounding.
1. 82 3
2. 435 219 121
3. 4286 2089
4. 99 12
5. 106 9
6. 192 39
Estimate by clustering.
7. 19 18 21 20 19
8. 498 499 502 503
9. 82 79 77 81
10. 4 3 6 5 7 4 6 7
Estimate by using compatible numbers.
11. 31 4
12. 17 82 58 43 75
13. 122 79 232 68
14. 205 6
15. 540 470 325 70
16. 813 9
Estimate by using front-end estimation.
17. 852 312
18. 65 4
19. 120 3
20. 895 246
21. 340 2
22. 673 344
23. 680 290
24. 647 9
25. 68 11
26. 99.6 18.25
27. 43 62 22 77
28. 69 72 68 70 73
29. 390 52
30. 102 6
31. 498 19
32. 493 183
33. 199 205 198
34. 999 52
35. 1209 403
36. 2005 4
37. 490 514 520 483
38. 3486 5
39. 7654 3254
40. 3045 124
41. 188 320
42. 12,250 4008
43. 874 523
Use any method to estimate.
Prerequisite Skills
593