Chapter Review
Hindu-Arabic Positional System
1.
What is the base of 57?
2.
What is the exponent of 57?
3.
Compute {4^5} + {3^2}.
4.
Convert the Hindu-Arabic number into expanded form: 4,201.
5.
Convert the expression to a Hindu-Arabic numeral: 6 \times {10^3} + 3 \times {10^2} + 7 \times {10^1} + 5 \times {10^0}.
Early Numeration Systems
6.
Which systems—Hindu-Arabic, Roman, Mayan, or Babylonian—are additive systems?
7.
Which systems—Hindu-Arabic, Roman, Mayan, or Babylonian—are positional systems?
8.
Which systems—Hindu-Arabic, Roman, Mayan, or Babylonian—use a 0?
9.
In the Babylonian system, what are the place values based on?
10.
In the Mayan system, what are the place values based on?
11.
Convert the Babylonian numeral to a Hindu-Arabic numeral.



12.
Convert the Mayan numeral to a Hindu-Arabic numeral.




13.
Convert the Roman numeral MMCDXLVII into a Hindu-Arabic numeral.
14.
Convert the Hindu-Arabic numeral 394 to a Roman numeral.
Converting with Base Systems
15.
List the numbers from 0 to 100 in base 5.
16.
In base 8, what is the place value of the 3 in the number 6388?
17.
How many symbols are needed for a base 17 system?
18.
What does it mean for a number to be in base 6?
19.
What symbols are used in a base 12 system?
20.
When converting from a base 10 number to a base 2 number, would the number of digits decrease?
21.
Convert 3115 to base 10.
22.
Convert 4512 to base 10.
23.
Convert 10012 to base 10.
24.
Convert 459 to base 8.
25.
Convert 1198 to base 12.
26.
Convert 38 to base 2.
27.
When converting from base 10 to base 4, the result obtained was 1424. How can you tell an error was made?
Addition and Subtraction in Base Systems
28.
Create the addition table for base 5.
29.
How many addition rules are there for a base 7 system?
30.
Calculate 345 + 445.
31.
Calculate A712 + 8812.
32.
Calculate 5416 − 2336.
33.
Calculate 5B12 − 1A12.
34.
When adding in base 8, the result 9118 is found. How do we know a mistake was made?
Multiplication and Division in Base Systems
35.
What is the process for creating the multiplication table for a base other than 10?
36.
Create the multiplication table for base 7.
37.
How many multiplication rules are there in a base 3 system?
38.
Calculate {14_7} \times {25_7}.
39.
Calculate {67_{12}} \times 3{{\text{B}}_{12}}.
40.
Calculate {42_7} \div {5_7}.
41.
Calculate {38_{12}} \div {{\text{B}}_{12}}.
42.
When multiplying {14_{12}} \times {10_{12}}, the result 140 is found. How do we know a mistake was made?