# 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
- 4
- 9
- 5
- 3

**Answer**-
- thousands
- hundreds
- tens
- ten thousands
- ones

##### Exercise \(\PageIndex{35}\)

87,210

- 2
- 8
- 0
- 7
- 1

##### Exercise \(\PageIndex{36}\)

164,285

- 5
- 6
- 1
- 8
- 2

**Answer**-
- ones
- ten thousands
- hundred thousands
- tens
- hundreds

##### Exercise \(\PageIndex{37}\)

395,076

- 5
- 3
- 7
- 0
- 9

##### Exercise \(\PageIndex{38}\)

93,285,170

- 9
- 8
- 7
- 5
- 3

**Answer**-
- ten millions
- ten thousands
- tens
- thousands
- millions

##### Exercise \(\PageIndex{39}\)

36,084,215

- 8
- 6
- 5
- 4
- 3

##### Exercise \(\PageIndex{40}\)

7,284,915,860,132

- 7
- 4
- 5
- 3
- 0

**Answer**-
- trillions
- billions
- millions
- tens
- thousands

##### Exercise \(\PageIndex{41}\)

2,850,361,159,433

- 9
- 8
- 6
- 4
- 2

In the following exercises, name each number using words.

##### Exercise \(\PageIndex{42}\)

1,078

**Answer**-
one thousand, seventy-eight

##### Exercise \(\PageIndex{43}\)

5,902

##### Exercise \(\PageIndex{44}\)

364,510

**Answer**-
three hundred sixty-four thousand, five hundred ten

##### Exercise \(\PageIndex{45}\)

146,023

##### Exercise \(\PageIndex{46}\)

5,846,103

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

##### Exercise \(\PageIndex{47}\)

1,458,398

##### Exercise \(\PageIndex{48}\)

37,889,005

**Answer**-
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

**Answer**-
412

##### Exercise \(\PageIndex{51}\)

two hundred fifty-three

##### Exercise \(\PageIndex{52}\)

thirty-five thousand, nine hundred seventy-five

**Answer**-
35,975

##### Exercise \(\PageIndex{53}\)

sixty-one thousand, four hundred fifteen

##### Exercise \(\PageIndex{54}\)

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

**Answer**-
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

**Answer**-
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.

- 386
- 2,931

**Answer**-
- 390
- 2,930

##### Exercise \(\PageIndex{59}\)

Round to the nearest ten.

- 792
- 5,647

##### Exercise \(\PageIndex{60}\)

Round to the nearest hundred.

- 13,748
- 391,794

**Answer**-
- 13,700
- 391,800

##### Exercise \(\PageIndex{61}\)

Round to the nearest hundred.

- 28,166
- 481,628

##### Exercise \(\PageIndex{62}\)

Round to the nearest ten.

- 1,492
- 1,497

**Answer**-
- 1,490
- 1,500

##### Exercise \(\PageIndex{63}\)

Round to the nearest ten.

- 2,791
- 2,795

##### Exercise \(\PageIndex{64}\)

Round to the nearest hundred.

- 63,994
- 63,940

**Answer**-
- 64,000
- 63,900

##### Exercise \(\PageIndex{65}\)

Round to the nearest hundred.

- 49,584
- 49,548

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

##### Exercise \(\PageIndex{66}\)

392,546

**Answer**-
- 392,500
- 393,000
- 390,000

##### Exercise \(\PageIndex{67}\)

619,348

##### Exercise \(\PageIndex{68}\)

2,586,991

**Answer**-
- 2,587,000
- 2,587,000
- 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

**Answer**-
divisible by 2, 3, and 6

##### Exercise \(\PageIndex{71}\)

9,696

##### Exercise \(\PageIndex{72}\)

75

**Answer**-
divisible by 3 and 5

##### Exercise \(\PageIndex{73}\)

78

##### Exercise \(\PageIndex{74}\)

900

**Answer**-
divisible by 2, 3, 5, 6, and 10

##### Exercise \(\PageIndex{75}\)

800

##### Exercise \(\PageIndex{76}\)

986

**Answer**-
divisible by 2

##### Exercise \(\PageIndex{77}\)

942

##### Exercise \(\PageIndex{78}\)

350

**Answer**-
divisible by 2, 5, and 10

##### Exercise \(\PageIndex{79}\)

550

##### Exercise \(\PageIndex{80}\)

22,335

**Answer**-
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

**Answer**-
\(2\cdot 43\)

##### Exercise \(\PageIndex{83}\)

78

##### Exercise \(\PageIndex{84}\)

132

**Answer**-
\(2\cdot 2\cdot 3\cdot 11\)

##### Exercise \(\PageIndex{85}\)

455

##### Exercise \(\PageIndex{86}\)

693

**Answer**-
\(3\cdot 3\cdot 7\cdot 11\)

##### Exercise \(\PageIndex{87}\)

400

##### Exercise \(\PageIndex{88}\)

432

**Answer**-
\(2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 3\)

##### Exercise \(\PageIndex{89}\)

627

##### Exercise \(\PageIndex{90}\)

2,160

**Answer**-
\(2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 3\cdot 5\)

##### 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

**Answer**-
24

##### Exercise \(\PageIndex{93}\)

4, 3

##### Exercise \(\PageIndex{94}\)

12, 16

**Answer**-
48

##### Exercise \(\PageIndex{95}\)

30, 40

##### Exercise \(\PageIndex{96}\)

20, 30

**Answer**-
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

**Answer**-
24

##### Exercise \(\PageIndex{99}\)

12, 16

##### Exercise \(\PageIndex{100}\)

28, 40

**Answer**-
280

##### Exercise \(\PageIndex{101}\)

84, 90

##### Exercise \(\PageIndex{102}\)

55, 88

**Answer**-
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

- ten
- hundred
- thousand; and
- ten-thousand.

**Answer**-
- $24,490
- $24,500
- $24,000
- $20,000

##### Exercise \(\PageIndex{107}\)

**Remodeling a Kitchen** Marissa’s kitchen remodeling cost $18,549, Round the cost to the nearest

- ten
- hundred
- thousand and
- 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

- billion
- hundred-million; and
- million.

**Answer**-
- 1,000,000,000
- 1,300,000,000
- 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

- hundred-million
- ten-million; and
- 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?

**Answer**-
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?

**Answer**-
Answers may vary.

##### 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.