### 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} \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?