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# 1.2E: Exercises

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## Practice Makes Perfect

Use Place Value with Whole Numbers

In the following exercises, find the place value of each digit in the given numbers.

Exercise $$\PageIndex{34}$$

51,493

1. 1
2. 4
3. 9
4. 5
5. 3
1. thousands
2. hundreds
3. tens
4. ten thousands
5. ones

Exercise $$\PageIndex{35}$$

87,210

1. 2
2. 8
3. 0
4. 7
5. 1

Exercise $$\PageIndex{36}$$

164,285

1. 5
2. 6
3. 1
4. 8
5. 2
1. ones
2. ten thousands
3. hundred thousands
4. tens
5. hundreds

Exercise $$\PageIndex{37}$$

395,076

1. 5
2. 3
3. 7
4. 0
5. 9

Exercise $$\PageIndex{38}$$

93,285,170

1. 9
2. 8
3. 7
4. 5
5. 3
1. ten millions
2. ten thousands
3. tens
4. thousands
5. millions

Exercise $$\PageIndex{39}$$

36,084,215

1. 8
2. 6
3. 5
4. 4
5. 3

Exercise $$\PageIndex{40}$$

7,284,915,860,132

1. 7
2. 4
3. 5
4. 3
5. 0
1. trillions
2. billions
3. millions
4. tens
5. thousands

Exercise $$\PageIndex{41}$$

2,850,361,159,433

1. 9
2. 8
3. 6
4. 4
5. 2

In the following exercises, name each number using words.

Exercise $$\PageIndex{42}$$

1,078

one thousand, seventy-eight

Exercise $$\PageIndex{43}$$

5,902

Exercise $$\PageIndex{44}$$

364,510

three hundred sixty-four thousand, five hundred ten

Exercise $$\PageIndex{45}$$

146,023

Exercise $$\PageIndex{46}$$

5,846,103

five million, eight hundred forty-six thousand, one hundred three

Exercise $$\PageIndex{47}$$

1,458,398

Exercise $$\PageIndex{48}$$

37,889,005

thirty-seven million, eight hundred eighty-nine thousand, five

Exercise $$\PageIndex{49}$$

62,008,465

In the following exercises, write each number as a whole number using digits.

Exercise $$\PageIndex{50}$$

four hundred twelve

412

Exercise $$\PageIndex{51}$$

two hundred fifty-three

Exercise $$\PageIndex{52}$$

thirty-five thousand, nine hundred seventy-five

35,975

Exercise $$\PageIndex{53}$$

sixty-one thousand, four hundred fifteen

Exercise $$\PageIndex{54}$$

eleven million, forty-four thousand, one hundred sixty-seven

11,044,167

Exercise $$\PageIndex{55}$$

eighteen million, one hundred two thousand, seven hundred eighty-three

Exercise $$\PageIndex{56}$$

three billion, two hundred twenty-six million, five hundred twelve thousand, seventeen

3,226,512,017

Exercise $$\PageIndex{57}$$

eleven billion, four hundred seventy-one million, thirty-six thousand, one hundred six

In the following, round to the indicated place value.

Exercise $$\PageIndex{58}$$

Round to the nearest ten.

1. 386
2. 2,931
1. 390
2. 2,930

Exercise $$\PageIndex{59}$$

Round to the nearest ten.

1. 792
2. 5,647

Exercise $$\PageIndex{60}$$

Round to the nearest hundred.

1. 13,748
2. 391,794
1. 13,700
2. 391,800

Exercise $$\PageIndex{61}$$

Round to the nearest hundred.

1. 28,166
2. 481,628

Exercise $$\PageIndex{62}$$

Round to the nearest ten.

1. 1,492
2. 1,497
1. 1,490
2. 1,500

Exercise $$\PageIndex{63}$$

Round to the nearest ten.

1. 2,791
2. 2,795

Exercise $$\PageIndex{64}$$

Round to the nearest hundred.

1. 63,994
2. 63,940
1. 64,000
2. 63,900

Exercise $$\PageIndex{65}$$

Round to the nearest hundred.

1. 49,584
2. 49,548

In the following exercises, round each number to the nearest ⓐ hundred, ⓑ thousand, ⓒ ten thousand.

Exercise $$\PageIndex{66}$$

392,546

1. 392,500
2. 393,000
3. 390,000

Exercise $$\PageIndex{67}$$

619,348

Exercise $$\PageIndex{68}$$

2,586,991

1. 2,587,000
2. 2,587,000
3. 2,590,000

Exercise $$\PageIndex{69}$$

4,287,965

Identify Multiples and Factors

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, 3, 5, 6, and 10.

Exercise $$\PageIndex{70}$$

84

divisible by 2, 3, and 6

Exercise $$\PageIndex{71}$$

9,696

Exercise $$\PageIndex{72}$$

75

divisible by 3 and 5

Exercise $$\PageIndex{73}$$

78

Exercise $$\PageIndex{74}$$

900

divisible by 2, 3, 5, 6, and 10

Exercise $$\PageIndex{75}$$

800

Exercise $$\PageIndex{76}$$

986

divisible by 2

Exercise $$\PageIndex{77}$$

942

Exercise $$\PageIndex{78}$$

350

divisible by 2, 5, and 10

Exercise $$\PageIndex{79}$$

550

Exercise $$\PageIndex{80}$$

22,335

divisible by 3 and 5

Exercise $$\PageIndex{81}$$

39,075

Find Prime Factorizations and Least Common Multiples

In the following exercises, find the prime factorization.

Exercise $$\PageIndex{82}$$

86

$$2\cdot 43$$

Exercise $$\PageIndex{83}$$

78

Exercise $$\PageIndex{84}$$

132

$$2\cdot 2\cdot 3\cdot 11$$

Exercise $$\PageIndex{85}$$

455

Exercise $$\PageIndex{86}$$

693

$$3\cdot 3\cdot 7\cdot 11$$

Exercise $$\PageIndex{87}$$

400

Exercise $$\PageIndex{88}$$

432

$$2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 3$$

Exercise $$\PageIndex{89}$$

627

Exercise $$\PageIndex{90}$$

2,160

$$2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 3\cdot 5$$

Exercise $$\PageIndex{91}$$

2,520

​​​​​​In the following exercises, find the least common multiple of the each pair of numbers using the multiples method.

Exercise $$\PageIndex{92}$$

8, 12

24

Exercise $$\PageIndex{93}$$

4, 3

Exercise $$\PageIndex{94}$$

12, 16

48

Exercise $$\PageIndex{95}$$

30, 40

Exercise $$\PageIndex{96}$$

20, 30

60

Exercise $$\PageIndex{97}$$

44, 55

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.

Exercise $$\PageIndex{98}$$

8, 12

24

Exercise $$\PageIndex{99}$$

12, 16

Exercise $$\PageIndex{100}$$

28, 40

280

Exercise $$\PageIndex{101}$$

84, 90

Exercise $$\PageIndex{102}$$

55, 88

440

Exercise $$\PageIndex{103}$$

60, 72

## Everyday Math

Exercise $$\PageIndex{104}$$

Writing a Check Jorge bought a car for $24,493. He paid for the car with a check. Write the purchase price in words. Answer twenty-four thousand, four hundred ninety-three dollars Exercise $$\PageIndex{105}$$ Writing a Check Marissa’s kitchen remodeling cost$18,549. She wrote a check to the contractor. Write the amount paid in words.

Exercise $$\PageIndex{106}$$

Buying a Car Jorge bought a car for $24,493. Round the price to the nearest 1. ten 2. hundred 3. thousand; and 4. ten-thousand. Answer 1.$24,490
2. $24,500 3.$24,000
4. $20,000 Exercise $$\PageIndex{107}$$ Remodeling a Kitchen Marissa’s kitchen remodeling cost$18,549, Round the cost to the nearest

1. ten
2. hundred
3. thousand and
4. ten-thousand.

Exercise $$\PageIndex{108}$$

Population The population of China was 1,339,724,852 on November 1, 2010. Round the population to the nearest

1. billion
2. hundred-million; and
3. million.
1. 1,000,000,000
2. 1,300,000,000
3. 1,340,000,000

Exercise $$\PageIndex{109}$$

Astronomy The average distance between Earth and the sun is 149,597,888 kilometers. Round the distance to the nearest

1. hundred-million
2. ten-million; and
3. million.

Exercise $$\PageIndex{110}$$

Grocery Shopping Hot dogs are sold in packages of 10, but hot dog buns come in packs of eight. What is the smallest number that makes the hot dogs and buns come out even?

40

Exercise $$\PageIndex{111}$$

Grocery Shopping Paper plates are sold in packages of 12 and party cups come in packs of eight. What is the smallest number that makes the plates and cups come out even?

## Writing Exercises

Exercise $$\PageIndex{112}$$

Give an everyday example where it helps to round numbers.

Exercise $$\PageIndex{113}$$

If a number is divisible by 2 and by 3 why is it also divisible by 6?

Exercise $$\PageIndex{114}$$

What is the difference between prime numbers and composite numbers?

Exercise $$\PageIndex{115}$$

Explain in your own words how to find the prime factorization of a composite number, using any method you prefer.

## Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. ⓑ If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.