Deck 2: The Number System

Question 1

Let's say there are 31 students in your class. If each student greeted and shook hands with every other student in the class, how many handshakes would there be? ​

A) 465
B) 310
C) 62
D) 93
E) 4495

Answer 1

465

Question 2

Convert the following number into base 10. 7 4 1 ₉

A) 252
B) 100
C) 5436
D) 612
E) 604

Answer 2

604

Question 3

In some dairy states, a kind of base 6 is used for shipping milk. Six cartons of milk make 1 box; 6 boxes make 1 crate, 6 crates make 1 flat, and 6 flats make 1 pallet. Thus, if someone said they had filled 4355, that would mean 4 flats, 3 crates, 5 boxes, and 5 cartons. ​ How many cartons of milk would this be in base 10? ​

A) 172 cartons
B) 1007 cartons
C) 1013 cartons
D) 31,787 cartons
E) 6042 cartons

Answer 3

1007 cartons

Question 4

Represent these base 10 amounts in Babylonian symbols. ​ 192 ​

A)
B)
C)
D)
E)

Question 5

Convert the following number into base 2. ​ 34 ​

A) 1 0 0 0 1 0
B) 1 0 0 0 1
C) 1 0 0 0 1 0 10
D) 11 0 0 0 1 0
E) 0 0 0 1 0 111

Question 6

For what base x is the statement true? ​ 135 ₁₀ = 3 4 3 _X ​

A) 7
B) 4
C) 6
D) 13
E) 5

Question 7

Find the base 10 equivalent of the following manipulative. ​ ​

A) 1517
B) 877
C) 436
D) 345
E) 187

Question 8

Translate the following base 10 number into ancient Greek notation. ​ 5550 ​

A)
B)
C)
D)
E)

Question 9

What number comes before 4 5 0 ₈ ? ​

A) 3 4 8 ₈
B) 4 4 9 ₈
C) 4 5 7 ₈
D) 4 4 7 ₈
E) 4 4 8 ₈

Question 10

Convert the following Roman numeral into base 10 notation. ​ DCXVII ​

A) 337
B) 115
C) 513
D) 617
E) 832

Question 11

What number comes after ? ​

A)
B)
C)
D)
E)

Question 12

Find the base 10 equivalent of the following numeral. ​ DCXVII ​

A) 92
B) 113
C) 617
D) 126
E) 1904

Question 13

Translate the following ancient Greek number into base 10. ​ Η H H Δ Δ Δ Δ Γ I I ​

A) 345
B) 330
C) 5550
D) 5555
E) 347

Question 14

How many tens are in 6500? ​

A) 65
B) 0
C) 650
D) 65,000
E) 650,000

Question 15

Is 164₇ an even or odd number? ​

A) odd
B) even

Question 16

Translate the following ancient Chinese numbers into base 10. ​ ​

A) 46
B) 12,345
C) 45
D) 346
E) 123

Question 17

Let's say there are 25 students in your class. If each student gives every other student a card, how many cards are distributed? ​

A) 600
B) 300
C) 650
D) 50
E) 625

Question 18

Translate the following base 10 number into ancient Chinese notation. ​ 346 ​

A)
B)
C)
D)
E)

Question 19

NASA keeps track of time using the following system: ​ Hours:Minutes:Seconds:Hundreths of a Second ​ Thus 4:2:5:6 would mean that the program is 4 hours, 2 minutes, 5.06 seconds from launch. Let's say that a launch was temporarily stopped at 8 : 56 : 20 : 19 and then later stopped at 10 : 58 : 23 : 17 . How much time had elapsed between the two stops? ​

A) 18 hours, 2 minutes, 3.36 seconds
B) 2 hours, 18 minutes, 3.02 seconds
C) 2 hours, 2 minutes, 2.98 seconds
D) 12 hours, 60 minutes, 2.98 seconds
E) 18 hours, 60 minutes, 2.64 seconds

Question 20

Represent the following base 10 number in expanded form. ​ 30,505 ​

A) 3 · 10 ⁴ + 5 · 10 ³ + 5
B) 3 · 10 ⁴ + 5 · 10 ² + 5
C) 3 · 10 ⁵ + 5 · 10 ² + 5
D) 3 · 10 ⁴ + 5 · 10 ³ + 5 · 10 ²
E) 3 · 10 ³ + 5 · 10 ² + 5 · 10

Question 21

Name a fraction between and that has a denominator of 7 . ​

A) ​
B)
C)
D)
E)

Question 22

Rewrite the following in standard form. ​ 8 · 10⁵ + 4 · 10⁴ + 9 ​ ​

A) 849,000
B) 8,490,000
C) 840,009
D) 84,009
E) 849

Question 23

Place the correct symbol < , or , > between the two numbers. ​ ​

A)
B) ​

Question 24

Find the greatest common factor (GCF) of the numbers 8, 36. ​

A) 72
B) 4
C) 1
D) 288
E) 8

Question 25

You have from 10:00 p.m. to 11:30 p.m. to do a project. At 10:34, what fraction of the project remains? ​

A) ​
B)
C)
D)
E)

Question 26

Find the prime factorization of the number 24. ​

A) 8·3
B) 2·2·3·3
C) 2·2·2·2
D) 2·2·2·3
E) 4·9

Question 27

Find the greatest common factor (GCF) of the numbers 10, 12, 36. ​

A) 1
B) 4320
C) 2
D) 180
E) 10

Question 28

What is the largest 3 digit number in base 4 ? ​

A) 12
B) 11
C) 16
D) 65
E) 63

Question 29

Place the correct symbol < , or , > between the two numbers. ​ ​

A)
B) ​

Question 30

Place the correct symbol < , or , > between the two numbers. ​ ​

A) ​
B) ​

Question 31

What is the largest square that can be used to fill a 63 by 28 rectangle? ​

A) 14 by 14
B) 63 by 63
C) 7 by 7
D) 28 by 28
E) 5 by 5

Question 32

Represent the following number in base 5 by sketching a manipulative. ​ 2405 ​

A)
B)
C)
D)
E)

Question 33

Find the prime factorization of the number 440 . ​

A) 4 ⋅ 275
B) 8 ⋅ 5 ⋅ 11
C) 2 ⋅ 4 ⋅ 121
D) 2 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ 11
E) 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 11

Question 34

Graph the numbers on the number line. -3 and 0 ​

A) ​
B) ​
C) ​ ​
D) ​
E) ​

Question 35

Write the fraction in simplest form. ​ ​

A) ​
B) 1
C) 0
D)
E) ​

Question 36

Find the greatest common factor (GCF) of the numbers 18 , 72 . ​

A) 4
B) 72
C) 18
D) 1296
E) 1

Question 37

Find all factors of the number 45 . ​

A) 1, 3 , 5 , 15 , 25 , 45
B) 1, 3 , 5 , 9 , 15 , 25 , 45
C) 1, 3 , 5 , 9 , 15 , 45
D) 3 , 5 , 15 , 25 , 45
E) 3 , 5 , 9 , 15 , 25 , 45

Question 38

What is the largest tank you could use to measure both 72 gallons of gasoline and 45 gallons of gasoline? ​

A) 5
B) 9
C) 18
D) 8
E) 10

Question 39

Find all factors of the number 441. ​

A) 1, 3, 7, 9, 21, 49, 147, 441
B) 1, 3, 7, 9, 21, 49, 63 , 441
C) 1, 3, 7, 9, 21, 49, 63, 147, 441
D) 1, 3, 7, 9, 21, 49, 63, 147
E) 3, 7, 9, 21, 49, 63, 147, 441

Question 40

Find the greatest common factor (GCF) of the numbers 24 , 30 , 36 . ​

A) 30
B) 720
C) 6
D) 24
E) 36

Question 41

Sam worked 4 days, 5 hours, and 55 minutes last week. Convert this to a decimal, that is, 4._ _ days. In this problem, one day is equal to 8 hours. Round your answer to two decimal places. ​

A) 5.54
B) 5.31
C) 4.25
D) 5.77
E) 4.74

Question 42

Round 95.0710 to the nearest whole number. ​

A) 91
B) 93
C) 95
D) 97
E) 92