Question 1

Convert the number to the indicated base.
-$120112210_{\text {three }}$ to base nine

Accepted Answer

A)  $15443_{\text {nine }}$ 
B)  $26083_{\text {nine }}$ 
C)  $61570_{\text {nine }}$ 
D)  $16483_{\text {nine }}$ 
A)  $15443_{\text {nine }}$ 
B)  $26083_{\text {nine }}$ 
C)  $61570_{\text {nine }}$ 
D)  $16483_{\text {nine }}$

Question 2

Use the requested method to find the product.
-92 ·44; use the lattice method

Accepted Answer

A) 4058 
B) 4148 
C) 4038 
D) 4048 
A) 4058 
B) 4148 
C) 4038 
D) 4048

Question 3

Find all positive solutions for the equation.
-x≡ 4 (mod 7)

Accepted Answer

A) {4, 8, 12, ...} 
B) {4, 11, 18, ...} 
C) {1, 18, 25, ...} 
D) {11, 18, 91, ...} 
A) {4, 8, 12, ...} 
B) {4, 11, 18, ...} 
C) {1, 18, 25, ...} 
D) {11, 18, 91, ...}

Question 4

Find all positive solutions for the equation.
-10x ≡1 (mod 10)

Accepted Answer

A) {1, 10, 15, ...} 
B) {2, 7, 12, ...} 
C) Identity 
D) None 
A) {1, 10, 15, ...} 
B) {2, 7, 12, ...} 
C) Identity 
D) None

Question 5

Convert the Roman numeral to Hindu-Arabic form
-$\overline{\overline{\mathrm{XIX}}}$

Accepted Answer

A)  $19,000,000$ 
B)  $99,000,000$ 
C)  99,000 
D)  19,000 
A)  $19,000,000$ 
B)  $99,000,000$ 
C)  99,000 
D)  19,000

Question 6

Perform the modular arithmetic operation.
-(46 + 37)(mod 7)

Accepted Answer

A) 7 
B) 5 
C) 11 
D) 6 
A) 7 
B) 5 
C) 11 
D) 6

Question 7

Convert the number to the indicated base.
-$6 \mathrm { E } _ { \text {sixteen } }$ to decimal

Accepted Answer

A)  110 
B)  1,760 
C)  74 
D)  174 
A)  110 
B)  1,760 
C)  74 
D)  174

Question 8

Convert the Hindu-Arabic numeral to Roman form.
-16,818

Accepted Answer

A)  $\overline { \text { XVIDCCC} }$ XVIII 
B)  $\overline { \text { XVIDCCCL} }$VIII 
C)  $\overline { \text { XVI } }$LXVIII 
D)  $\overline { \text { XVI} }$DCCCXVIII 
A)  $\overline { \text { XVIDCCC} }$ XVIII 
B)  $\overline { \text { XVIDCCCL} }$VIII 
C)  $\overline { \text { XVI } }$LXVIII 
D)  $\overline { \text { XVI} }$DCCCXVIII

Question 9

Convert the decimal number to the given base.
-68 to base eight

Accepted Answer

A)  $104 _\text { eight }$ 
B) $102 _\text { eight }$ 
C)  $120 _\text { eight }$ 
D)  $140_\text { eight }$ 
A)  $104 _\text { eight }$ 
B) $102 _\text { eight }$ 
C)  $120 _\text { eight }$ 
D)  $140_\text { eight }$

Question 10

Convert the decimal number to the given base.
-503 to base five

Accepted Answer

A)  $4030 _\text { five }$ 
B)  $3004_\text { five }$ 
C)  $3040 _\text { five }$ 
D) $4003_\text { five }$ 
A)  $4030 _\text { five }$ 
B)  $3004_\text { five }$ 
C)  $3040 _\text { five }$ 
D) $4003_\text { five }$

Question 11

Identify the numeral as Babylonian, Mayan, or Greek. Give the equivalent in the Hindu-Arabic system.
-$\beta$
 $\mathrm { M } , \delta \psi \pi \eta$

Accepted Answer

A)  Greek; 24,788 
B)  Mayan; 3188 
C)  Greek; 2488 
D)  Greek; 24,798 
A)  Greek; 24,788 
B)  Mayan; 3188 
C)  Greek; 2488 
D)  Greek; 24,798

Question 12

Write the number as a Babylonian numeral.
-53

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Write (in the same base) the counting numbers just before and just after 13 eight

Accepted Answer

A)  $12 _ { \text {eight } }$ $15 _ { \text {eight } }$ 
B)  $10 _ { \text {eight } }$ $12 _ { \text {eight } }$ 
C)  $A _ { \text {eight } }$ $C _ { \text {eight } }$ 
D)  $12 _ { \text {eight } }$, $14 _ { \text {eight } }$ 
A)  $12 _ { \text {eight } }$ $15 _ { \text {eight } }$ 
B)  $10 _ { \text {eight } }$ $12 _ { \text {eight } }$ 
C)  $A _ { \text {eight } }$ $C _ { \text {eight } }$ 
D)  $12 _ { \text {eight } }$, $14 _ { \text {eight } }$

Question 14

Write the number as a Greek numeral.
-88

Accepted Answer

A)  $\circ \eta$ 
B)  $\pi \eta$ 
C)  $\pi \theta$ 
D)  $\circ \theta$ 
A)  $\circ \eta$ 
B)  $\pi \eta$ 
C)  $\pi \theta$ 
D)  $\circ \theta$

Question 15

The following formula can be used to find the day of the week on which a given year begins. First calculate
$\mathrm { a } = \mathrm { y } + \llbracket ( \mathrm { y } - 1 ) / 4 \rrbracket - \llbracket ( \mathrm { y } - 1 ) / 100 \rrbracket + \llbracket ( \mathrm { y } - 1 ) / 400 \rrbracket \text {, }$
where $y$ represents the year and $\llbracket x \rrbracket$ represents the greatest integer less than or equal to $x$. After finding $a$, find the smallest nonnegative integer $b$ such that
$a \equiv b ( \bmod 7 )$ Then $b$ gives the day of January 1, with $b = 0$ representing Sunday, $b = 1$ Monday and so on. Find the day of the week on which January 1 would occur in the year $2030 .$

Accepted Answer

A)  Tuesday 
B)  Wednesday 
C)  Sunday 
D)  Monday 
A)  Tuesday 
B)  Wednesday 
C)  Sunday 
D)  Monday

Question 16

Decide whether the statement is true or false.
-A base five numeral is divisible by 5 if and only if its ones digit is 0.

Accepted Answer

A) True 
 B)False

Question 17

Convert the Hindu-Arabic numeral to Egyptian form.
-367

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 18

Identify the largest number expressible in a simple grouping system with the specified base and specified number of distinct symbols.
-base $b$, eight distinct symbols (where $b$ is any counting number 2 or greater)

Accepted Answer

A)  $8 ^ { b } - 1$ 
B)  $b ^ { 8 } - 1$ 
C)  $b ^ { 8 }$ 
D)  $8 \mathrm {~b} - 1$ 
A)  $8 ^ { b } - 1$ 
B)  $b ^ { 8 } - 1$ 
C)  $b ^ { 8 }$ 
D)  $8 \mathrm {~b} - 1$

Question 19

Convert the Egyptian numeral to Hindu-Arabic form.
-

Accepted Answer

A)  240,006 
B)  246 
C)  2,000,046 
D)  2406 
A)  240,006 
B)  246 
C)  2,000,046 
D)  2406

Question 20

Convert the number to binary form.
-7603 eight

Accepted Answer

A)  $100001111101 _ { \text {two } }$ 
B)  $111110000011 _ { \text {two } }$ 
C)   $111110000010 _ { \text {two } }$ 
D)  $100001111100 _ { \text {two } }$ 
A)  $100001111101 _ { \text {two } }$ 
B)  $111110000011 _ { \text {two } }$ 
C)   $111110000010 _ { \text {two } }$ 
D)  $100001111100 _ { \text {two } }$

Convert the number to the indicated base. - $120112210_{\text {three }}$ to base nine

Use the requested method to find the product. -92 ·44; use the lattice method

Find all positive solutions for the equation. -x≡ 4 (mod 7)

Find all positive solutions for the equation. -10x ≡1 (mod 10)

Convert the Roman numeral to Hindu-Arabic form - $\overline{\overline{\mathrm{XIX}}}$

Perform the modular arithmetic operation. -(46 + 37)(mod 7)

Convert the number to the indicated base. - $6 \mathrm { E } _ { \text {sixteen } }$ to decimal

Convert the Hindu-Arabic numeral to Roman form. -16,818

Convert the decimal number to the given base. -68 to base eight

Convert the decimal number to the given base. -503 to base five

Identify the numeral as Babylonian, Mayan, or Greek. Give the equivalent in the Hindu-Arabic system. - $\beta$ $\mathrm { M } , \delta \psi \pi \eta$

Write the number as a Babylonian numeral. -53

Write (in the same base) the counting numbers just before and just after 13_eight

Write the number as a Greek numeral. -88

Decide whether the statement is true or false. -A base five numeral is divisible by 5 if and only if its ones digit is 0.

Convert the Hindu-Arabic numeral to Egyptian form. -367

Identify the largest number expressible in a simple grouping system with the specified base and specified number of distinct symbols. -base $b$ , eight distinct symbols (where $b$ is any counting number 2 or greater)

Convert the Egyptian numeral to Hindu-Arabic form. -

Convert the number to binary form. -7603 eight

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Exam 4: Numeration Systems

Convert the number to the indicated base. - 120112210three 120112210_{\text {three }}120112210three ​ to base nine