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28 Topic 1

Reteaching

1-1Place Value

A parsec is a unit of measurement equal to 30,860,000,000,000 kilometers. Each digit in the number 30,860,000,000,000 has a place value. The 3 in the number is in the ten-trillions place, and the value is 30,000,000,000,000. A comma separates the number into periods.

The number 30,860,000,000,000 can be written in different ways.

Standard form: 30,860,000,000,000

Word form: Thirty trillion, eight hundred sixty billion

Expanded form: 30,000,000,000,000 � 800,000,000,000 � 60,000,000,000

Strategy Practice For 1–3, write each number in the place-value chart above. Then write the place and the value of the underlined digit.

1. 1,234,567,890

2. 568,103,528,492

3. 12,400,221,000,445

4. Write 4,200,060,000 in word form. Use the place-value chart for help.

5. Write fifteen trillion, four hundred thousand in standard form.

6. Lake Argyle normally holds about two hundred billion, four hundred million cubic feet of water. Write this number in expanded form.

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Four billion, two hundred million, sixty thousand

Millions, 4,000,000

Ten billions, 60,000,000,000

Ten trillions, 10,000,000,000,000

15,000,000,400,000

200,000,000,000 � 400,000,000

1 2 3 4 5 6 7 8 9 0 5 6 8 1 0 3 5 2 8 4 9 2 1 2 4 0 0 2 2 1 0 0 0 4 4 5

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1-1Place ValueFor 1–4, write the place and the value of the underlined digit.

1. 205,300,005,001

2. 680,525,917,143

3. 102,105,000,071,000

4. 40,400,040,000,444

5. Write the number 100,050,000,982 in expanded form using only addition.

6. What is 23,000,400,000,158 in word form?

A Twenty-three million, four hundred thousand, one hundred fifty-eight

B Twenty-three billion, four hundred million, one hundred fifty-eight

C Twenty-three trillion, four hundred million, one hundred fifty-eight

D Two trillion, three billion, four million, one hundred fifty-eight

7. Algebra A megabyte holds about 1,000,000 characters of data. A gigabyte holds about 1,000 times as much data as a megabyte. About how many characters of data does the gigabyte hold?

A One trillion

B One billion

C One million

D One thousand

8. Writing to Explain How are the labels in each period alike? How are they different?

Practice 1-1

Ten trillions, 10,000,000,000,000

Billions, 5,000,000,000Hundred billions, 600,000,000,000Trillions, 2,000,000,000,000

100,000,000,000 50,000,000 900 80 2

Ten millions, 40,000,000

Sample answer: Each period has hundreds, tens, and units in order from left to right. The values are different for each period.

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34 Topic 1

Comparing and Ordering Whole Numbers

Three whales weigh 112,290 pounds, 112,238 pounds, and 112,336 pounds. You can use a place-value chart to order the weights from greatest to least.

Write the numbers in the place-value chart.

Start with the greatest place. Find the first place where the digits are different. That is the hundreds place. Since 3 is greater than 2 112,336 is the greatest weight. Compare the tens place for the other two weights. The weights in order are: 112,336; 112,290; 112,238.

Use < or > to compare.

1. 7,210 7,201 2. 18,336 23,214 3. 46,177 46,195

4. 326,251 316,622 5. 982,315 1,200,551 6. 6,832,525 8,832,114

For 7 and 8, order the numbers from least to greatest.

7. 36,352; 42,177; 36,890

8. 472,315,000; 471,278,000; 477,515,000

9. Number Sense If you compare a 4-digit whole number and a 5-digit whole number, which number is greater?

Reteaching

1-2Re

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1-2

<> <<>

36,352; 36,890; 42,177

471,278,000; 472,315,000; 477,515,000

The 5-digit number

<

1 1 2 2 9 01 1 2 2 3 81 1 2 3 3 6

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Topic 1 35

Comparing and Ordering Whole NumbersUse < or > to compare.

1. 9,035 9,062 2. 362,286 360,055 3. 7,261,005 7,266,500

For 4 and 5, order the numbers from least to greatest.

4. 75,321; 72,369; 72,752; 57,575

5. 6,074,232; 6,234,921; 6,243,219

For 6 and 7, order from greatest to least.

6. 300 thousand; 300 billion; 3 trillion; 30 million

7. 4,810,414; 4,767,894; 4,562,626; 4,909,000

8. Writing to Explain Tell how you would decide if 9,899,989 is greater than or less than 9,898,998.

9. Number Sense If you plot these numbers on a number line, which one will be in the middle? 105,394; 150,494; 115,054

10. Geometry Which of these figures has the greatest perimeter?

A A square with sides 109 meters long

B A hexagon with sides 65 meters long

C A rectangle with length 24 meters and width 46 meters

D A pentagon with sides 72 meters long

Practice

1-2Practice 1

-2

<< >

57,575; 72,369; 72,752; 75,321

6,074,232; 6,234,921; 6,243,219

3 trillion; 300 billion; 30 million; 300 thousand

4,909,000; 4,810,414; 4,767,894; 4,562,626

Start at millions place. Look at the digits ineach place. In thousands place the digits are different. Compare: 9 > 8 so 9,899,989 > 9,898,998.

115,054

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40 Topic 1

Exponents and Place Value

base 54 exponent

The number 5 is the base. The base is the factor that is being multiplied.

The number 4 is the exponent. The exponent tells how many times the base is used as a factor.

54 � 5 � 5 � 5 � 5 � 625

The base (5) is used as a factor the exponent (4) number of times.

To write a product in exponential form: 4 � 4 � 4 � 4 � 4 � 4 � 4

First write the base: 4

Count the number of times the base is used as a factor. This is the exponent. 47

To evaluate an exponential number: 63

Write the base as a factor the number of times shown by the exponent.

63 � 6 � 6 � 6 � 216

To write the expanded form of a number using exponents:

Write the number in expanded form.

52,965 � (5 � 10,000) � (2 × 1,000) � (9 � 100) � (6 � 10) � (5 � 1)

Write the place values as powers of 10.

52,965 � (5 � 104) � (2 � 103) � (9 � 102) � (6 � 101) � (5 � 100)

Tip: Any number raised to the first power equals that number. 81 � 8

Write each power as a product and evaluate the expression.

1. 94 2. 45

Write each product in exponential form.

3. 3 � 3 � 3 � 3 � 3 4. 7 � 7 � 7 � 7 � 7 � 7 � 7 � 7

Write the number in expanded form using exponents.

5. 74,271 � � � � �

6. Number Sense Explain the difference between 46 and 64.

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9 � 9 � 9 � 9 � 6,561 4 � 4 � 4 � 4 � 4 � 1,024

35 78

(7�104) (4�103) (2�102) (7�101) (1�100)

46 means 4 � 4 � 4 � 4 � 4 � 4 � 4,096

and 64 means 6 � 6 � 6 � 6 � 1,296.

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Topic 1 41

ExponentsandPlaceValueWrite each expression in exponential form.

1. 5 3 5 3 5 3 5 3 5 3 5 2. 2 3 2 3 2 3 2 3 2 3 2 3 2

3. 3 3 3 3 3 4. 9

Write each number in expanded form using exponents.

5. 53,806

6. 527,519

Evaluate.

7. 62 8. 53 9. 36 10. 28

11. Reasoning Zach invested $50 and was able to triple his money in two years. Kayla also began with $50 in investments, and was able to cube her money in two years. Who had more money after two years? Explain.

12. WritingtoExplain In 1968, the estimated population of the world was 3,559,028,982 people. When this number is written in expanded form using exponents, one power of 10 would not be represented. Which power of 10? Why?

13. NumberSense Which is NOT equal to 1?

A 100

B 41

C 1 3 100

D 14

Practice 1-3

Practice

1-3

56 27

33 91

(5104)(3103)(8102)(6100) (5105)(2104)(7103) (5102) (1101)(9100)

36 125 729 256

Kaylahadmoremoney,becauseshehad$503,or505050$125,000.Zachonlyhad$503$150aftertwoyears.

105wouldnotberepresentedbecausethereisa0inthehundred-thousandsplace.

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Reteaching

1-4Decimal Place ValueA decimal is a number that uses a decimal point. Each digit in a decimal number has a place and value. You can use a place-value chart to determine a digit’s place and value. The decimal point is read “and”.

ones decimals

5

hund

reds tens

ones

ten th

ousa

ndths

hund

red

thous

andt

hs

tenths

hund

redt

hstho

usan

dths

. 2 6 8 4

and

The 8 is in the thousandths place. Its value is 8 thousandths, or 0.008.

The standard form of the number is 5.2684. The word form is five and two thousand, six hundred eighty-four ten thousandths.

The expanded form is: 1 0.2 1 0.06 1 1 0.0004.

Write the place and value of the underlined digit.

1. 2.195

2. 6.2394

3. 34.3262

Write the number given in the form indicated.

4. 2.346 in short-word form

5. 13 and 223 thousandths in standard form

6. 281.1025 in word form

7. Number Sense Write a decimal that has 3 in thetenths place and 1 in the ten thousandths place.

8. Writing to Explain Explain how you know that 17 thousandths has more than two places to the right of the decimal point.

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5 0.008

Thousandths, 0.005Hundredths, 0.03Ten thousandths, 0.0002

2 and 346 thousandths13.223

Two hundred eighty-one and one thousand twenty-five ten thousandths

Sample answer: 2.3451

Sample answer: The thousandths place is threedigits to the right of the decimal point.

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1-4Decimal Place ValueWrite the place and value of the underlined digit.

1. 56.389

2. 9.64372

Write the number given in the form indicated.

3. 8.7204 in expanded form

4. 43 and 962 ten thousandths in standard form

What is the whole number portion of the decimal?

5. 5.024 6. 418.0972

What is the decimal portion of the decimal?

7. 176.261 8. 91.0213

The slowest growing tree is a White Cedar in Canada. It grew about 0.0658 centimeters per year in 155 years. Use this information to answer 9 and 10.

9. To what decimal place value is the yearly growth measured?

10. How would you write this number in word form?

11. Number Sense Write a decimal that has 6 in thehundredths place and the ten thousandths place.

12. Writing to Explain How would you write adecimal that is less than 5 ten thousandths?

13. Which shows the short-word form for 16.011?

A 16 and 11 thousandths B 16 and 11 ten thousandths

C 16 and 11 hundredths D 16 and 11 tenths

Practice 1-4

Hundredths, 0.08Ten thousandths, 0.0007

(831)1(730.1)1(230.01)1(430.0001)

43.0962

5 418

0.261 0.0213

Ten thousandths

Six hundred fifty-eight ten thousandthsSample answer:12.3646

Youwouldwritezerointhetenths,hundredths,andthousandthsplacesandanumberlessthan5intheten thousandthsplace

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52 Topic 1

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Reteaching

1-5Multiplying and Dividing by 10, 100, and 1,000

You can use place value and patterns to multiply and divide by 10, 100, and 1,000.

Multiplying by 10, 100, and 1,000

Move the decimal point the same number of places to the right as there are zeros. Annex zeros if you need to.

1.12 × 10 = 11.2 The decimal point moves 1 place to the right.0.2 × 100 = 20 The decimal point moves 2 places to the right.0.006 × 1,000 = 6 The decimal point moves 3 places to the right.

Dividing by 10, 100, and 1,000

Move the decimal point the same number of places to the left as there are zeros. Annex zeros if you need to.

0.2 ÷ 10 = 0.02 The decimal point moves 1 place to the left.1.08 ÷ 100 = 0.0108 The decimal point moves 2 places to the left.170 ÷ 1,000 = 0.17 The decimal point moves 3 places to the left.

Find each product or quotient.

1. 0.31 � 10 � 2. 1.51 � 100 �

3. 4.061 � 1,000 � 4. 2.6 � 10 �

5. 142.1 � 100 � 6. 50.5 � 1,000 �

7. 0.01 � 100 � 8. 30.63 � 10 �

9. 321.2 � 1,000 � 10. 4.59 � 10 �

11. 0.62 � 1,000 � 12. 0.8 � 100 �

13. Number Sense Without dividing, will the quotient be greater than or less than the dividend when you divide 0.34 by 10? Explain.

3.1 151

4,061 0.26

1.421 0.0505

1 3.063

0.3212 45.9

620 0.008

The quotient will be less than the dividend because the decimal point moves one place to the left when you divide by 10.

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Topic 1 53

Practice 1-5

Practice

1-5Multiplying and Dividing by 10, 100, and 1,000Find each product or quotient.

1. 0.006 3 10 5 2. 0.64 4 10 5

3. 123.3 4 100 5 4. 8.7 3 100 5

5. 0.145 3 1,000 5 6. 542.3 4 1,000 5

7. 0.91 3 100 5 8. 0.1 4 10 5

9. 100 4 1,000 5 10. 2 4 100 5

11. 0.302 3 1,000 5 12. 1.397 3 100 5

13. 0.038 4 10 5 14. 0.0115 3 10 5

15. Reasoning What number do you need to multiply by 100 to get the same result as 16.2 4 10? Explain.

16. Number Sense An alligator hatchling grew to 72.5 inches after six years. This length is 10 times its hatchling length. If you want to know its hatchling length, should you multiply or divide 72.5 by 10? Explain.

17. What is the quotient of 12.12 4 100?

A 0.1212

B 1.212

C 121.2

D 1,212

18. Writing to Explain Casey said that 0.03 3 1,000 is 3. Explain why Casey’s answer is not correct. What mistake do you think he made?

0.06 0.064 1.233 870 145 0.5423 91 0.01 0.1 0.02 302 139.7 0.0038 0.115

0.0162; since 16.2 ÷ 10 = 1.62, and multiplication and division are inverse operations, you can divide 1.62 by 100 to give 0.0162, which is 1.62 when you multiply it by 100.

Divide; sample answer: The hatchling length is less than the 6-year length, so you divide to get a length less than 72.5.

When multiplying by 1,000, you need to move the decimal point 3 places to the right, so the correct answer is 30. Casey forgot to annex a zero.

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Reteaching

1-6Comparing and Ordering Decimals

Compare decimals 6.241 The digit in the hundredthsby place value. 6.285 place shows which is greater.

6.285 . 6.241

Order decimals on a number line.

Order 3.572, 3.746, and 3.719 from least to greatest.

3.6

3.572

3.5 3.8

3.719

3.7

3.746

Order decimals by place value.

Order 5.337, 6.278, 5.185, and 5.319 from least to greatest.

Order by ones: 5.337 5.185 5.319 6.278

Order by tenths. 5.185 5.337 5.319 6.278

Order by hundredths. 5.185 5.319 5.337 6.278

5.185 , 5.319 , 5.337, 6.278

Use ., ,, or 5 to compare each pair of numbers.

1. 0.57 0.75 2. 2.382 2.283

3. 4.8693 4.8963 4. 3.6720 3.0672

Order from least to greatest.

5. 1.943 1.869 1.895

6. 6.584 6.579 6.568

7. 4.704 4.74 4.074

8. 3.5603 3.5063 3.0563

9. Writing to Explain Explain how you know which number is greater 2.094 or 2.904.

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-6

1.869, 1.895, 1.9436.568, 6.579, 6.5844.074, 4.704, 4.743.0563, 3.5063, 3.5603

2.094 has 2 ones, no tenths, 9 hundredths, and 4 thousandths.2.904 has 2 ones, 9 tenths, no hundredths, and 4 thousandths.Two ones and 9 tenths is greater than 2 ones and no tenths.

><><

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Topic 1 59

Practice

1-6Comparing and Ordering DecimalsUse >, <, or = to compare each pair of numbers.

1. 656.07 656.23 2. 73.42 72.56

3. 0.01 0.10 4. 7.999 7.998

Order from least to greatest.

5. 639.087, 639.078, 639.088

6. 0.0909, 0.0989, 0.0999

7. Geometry Which circle has the greatest diameter? (The diameter is the line through the center of a circle.)

8. Writing to Explain How would you find a number between 3.2 and 3.26?

9. Which decimal is greater than 3.33 but less than 3.34?

A 2.3349

B 3.305

C 3.329

D 3.336

Practice 1-6

< >< >

639.078, 639.087, 639.088

0.0909, 0.0989, 0.0999

Circle C

The tenths of the two numbers are the same, so I need to finda number that has the same ones and tenths, but has less than 6 hundredths, such as 3.24.

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64 Topic 1

Reteaching

1-7Problem Solving: Make an Organized List

Jose, Sumi, and Tina need to stand in a straight line in the school cafeteria. In how many different ways can they stand in the line?

Read and Understand

Step 1: What do you know?

Jose, Sumi, and Tina need to be

in a straight line.

Step 2: What are you trying to find?

How many different ways can the

three friends stand in the line?

Plan and Solve

Step 3: Make an organized list to find the different ways Jose, Sumi, and Tina can stand in the line.

Jose First Sumi First Tina First

Jose, Sumi, Tina Sumi, Jose, Tina Tina, Jose, Sumi

Jose, Tina, Sumi Sumi, Tina, Jose Tina, Sumi, Jose

Answer: Jose, Sumi, and Tina can stand in the line in 6 different ways.

Solve by making an organized list. The lists have been started for you. Finish the lists.

1. Brandon is using the digits 2, 3, 6, and 9 for his locker. How many different combinations can he make using the four digits?

2 3 6 9

2369 3269 6239 9236

2396 3296 6293 9263

2 93 3692 6392 9326

263 3629 6329 9362

2936 3962 6923 9623

2963 3926 6932 9632

2. How many different pairs of markers can be formed if you have one yellow, one red, one green, one blue, and one purple marker?

Yellow Red Green Blue Purple

Y, R

Y, G

Y,

Y,

R, G

R, B

R, P

G, B

G, P

B, P

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24 different

combinations

10 different

pairs

69

BP

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1-7Practice 1

-7

Problem Solving: Make an Organized ListSolve by making an organized list. The lists have been started for you. Complete the lists and answer the questions.

1. A balloon game at the county fair gives 1,000 points, 500 points, and 250 points for each balloon that you pop. If Stewart buys 2 darts and pops 2 balloons, how many possible points can he score?

1,000 500 250 Total✓ ✓ 2,000

✓ ✓ 1,500

✓ ✓ 1,250

2. How many different 3-letter arrangements can you make with the letters, L, G, and F?

L G F

LGF

LFG

3. In a chess tournament, Miguel, Rebecca, Kyle, Ana, and Josh will play each other once. How many games will they play?

M R K A JMR

MK

MA

MJ

4. Tanya has to wear a cap and T-shirt for her job at the amusement park. She can wear a red, blue, or yellow cap and a red or green shirt. How many different cap and shirt pairs can Tanya wear?

A 5 B 6 C 9 D 10

5. Writing to Explain How could you find the number of different arrangements of 6 letters in a computer password?

6 different scoresare possible.

6 different arrangements

10 games

Make a list using each of the 6 letters of the password as the first letter, with the remaining letters arranged in different orders.

✓✓ 1,000✓ ✓ 750 ✓✓ 500

GFL FLGGLF FGL

RK KA AJRA KJRJ

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