### Chapter Review

## Hindu-Arabic Positional System

1
.

What is the base of 5

^{7}?2
.

What is the exponent of 5

^{7}?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 638

_{8}?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 311

_{5}to base 10.22
.

Convert 45

_{12}to base 10.23
.

Convert 1001

_{2}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 142

_{4}. 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 34

_{5}+ 44_{5}.31
.

Calculate A7

_{12}+ 88_{12.}32
.

Calculate 541

_{6}− 233_{6.}33
.

Calculate 5B

_{12}− 1A_{12.}34
.

When adding in base 8, the result 911

_{8}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 ${42}_{7}\xf7{5}_{7}$.

41
.

Calculate ${38}_{12}\xf7{\text{B}}_{12}$.

42
.

When multiplying ${14}_{12}\times {10}_{12}$, the result 140 is found. How do we know a mistake was made?