Contemporary Mathematics

# 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?
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