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Mathematics LibreTexts

1.2E: Exercises

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    30453
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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
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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

    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.

    1. 386
    2. 2,931
    Answer
    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
    Answer
    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
    Answer
    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
    Answer
    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

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

    Exercise \(\PageIndex{67}\)

    619,348

    Exercise \(\PageIndex{68}\)

    2,586,991

    Answer
    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

    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

    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.
    Answer
    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?

    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.

    A table with four columns and four rows is shown. The columns are titled “I can …”, “Confidently”, “With some help”, and “No – I don’t get it!”. The first column has three rows of text that read “use place value with whole numbers”, “identify multiples and apply divisibility rules” and “find prime factorization and least common multiples”. All other spaces on the table are blank.

    ⓑ 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.