4.5.4: Chapter Review
Hindu-Arabic Positional System
What is the base of \(5^7\) ?
What is the exponent of \(5^7\) ?
Compute \(4^5+3^2\).
Convert the Hindu-Arabic number into expanded form: 4,201.
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
Which systems—Hindu-Arabic, Roman, Mayan, or Babylonian—are additive systems?
Which systems—Hindu-Arabic, Roman, Mayan, or Babylonian—are positional systems?
Which systems—Hindu-Arabic, Roman, Mayan, or Babylonian—use a 0?
In the Babylonian system, what are the place values based on?
In the Mayan system, what are the place values based on?
Convert the Babylonian numeral to a Hindu-Arabic numeral.
Convert the Mayan numeral to a Hindu-Arabic numeral.
Convert the Roman numeral MMCDXLVII into a Hindu-Arabic numeral.
Convert the Hindu-Arabic numeral 394 to a Roman numeral.
Converting with Base Systems
List the numbers from 0 to 100 in base 5.
In base 8, what is the place value of the 3 in the number 638 8 ?
How many symbols are needed for a base 17 system?
What does it mean for a number to be in base 6?
What symbols are used in a base 12 system?
When converting from a base 10 number to a base 2 number, would the number of digits decrease?
Convert 311 5 to base 10.
Convert 45 12 to base 10.
Convert 1001 2 to base 10.
Convert 459 to base 8.
Convert 1198 to base 12.
Convert 38 to base 2.
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
Create the addition table for base 5.
How many addition rules are there for a base 7 system?
Calculate 34 5 + 44 5 .
Calculate A7 12 + 88 12.
Calculate 541 6 − 233 6.
Calculate 5B 12 − 1A 12 .
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
What is the process for creating the multiplication table for a base other than 10 ?
Create the multiplication table for base 7.
How many multiplication rules are there in a base 3 system?
Calculate \(14_7 \times 25_7\).
Calculate \(67_{12} \times 3 B_{12}\).
Calculate \(42_7 \div 5_7\).
Calculate \(38_{12} \div \mathrm{B}_{12}\).
When multiplying \(14_{12} \times 10_{12}\), the result 140 is found. How do we know a mistake was made?