Understanding Numeration Systems: From Ancient to Modern

1) What is the Hindu-Arabic Numeration Form characterized by?

-base 10-place values are power of 10 (expanded)-method used today[developed the concept zero as a placeholder]

Roman numerals are used for calculations and counting.

Binary system with place values as powers of 2 is commonly used worldwide.

Hexadecimal system where base 16 is used for representing numbers is the most predominant form of numeration.

The Hindu-Arabic Numeration Form is known for its base 10-place values representing powers of 10 and is widely used today after developing the concept of zero as a placeholder.

Explanation

The Hindu-Arabic Numeration Form is known for its base 10-place values representing powers of 10 and is widely used today after developing the concept of zero as a placeholder.

2) What concrete model is commonly used to represent Base Ten Blocks?

-the Roman numeral model

-the Hindu-Arabic concrete model

-the binary concrete model

-the Mayan numerical system model

Base Ten Blocks are typically represented using the Hindu-Arabic concrete model, which is the decimal numeral system we commonly use in everyday life. The Roman numeral model, binary concrete model, and Mayan numerical system model do not align with the traditional Base Ten Blocks representation.

Explanation

Base Ten Blocks are typically represented using the Hindu-Arabic concrete model, which is the decimal numeral system we commonly use in everyday life. The Roman numeral model, binary concrete model, and Mayan numerical system model do not align with the traditional Base Ten Blocks representation.

3) What is the Tally Numeration Form used for?

A form of numeration specifically designed for advanced mathematics.

A method for complex calculations involving large numbers.

-used for simple, small counting-slash mark (/) represents grouping[shortest time frame counting method]

An ancient writing system used by civilizations for recordkeeping.

The Tally Numeration Form is primarily utilized for simple and small counting tasks, where a slash mark (/) is used to represent grouping, making it an efficient method for counting in short time frames.

Explanation

The Tally Numeration Form is primarily utilized for simple and small counting tasks, where a slash mark (/) is used to represent grouping, making it an efficient method for counting in short time frames.

4) What is the Egyptian Numeration Form?

B) A system of numeration based on hieroglyphics.

-play on Hindu-Arabic-symbols represent base 10 values[expanded the Tally Method Base 10]

D) A method of counting using only odd numbers.

C) A form of tallying numbers using symbols from ancient Mesopotamia.

A) An ancient form of Roman numerals used in Egypt.

The Egyptian Numeration Form is a numerical system that utilized symbols similar to Hindu-Arabic numerals to represent base 10 values, expanding on the Tally Method in base 10.

Explanation

The Egyptian Numeration Form is a numerical system that utilized symbols similar to Hindu-Arabic numerals to represent base 10 values, expanding on the Tally Method in base 10.

5) What form of numeration was used by the Babylonians?

Base 10 counting system with zero as a placeholder

Base 5 counting system with symbols representing powers of 5

Binary-based numeration system

The Babylonians used a Base 60 counting system, put spaces between to represent the powers of 60, and did not have zero as a placeholder. This system was developed around the same time as the Egyptian numeration system.

Explanation

The Babylonians used a Base 60 counting system, put spaces between to represent the powers of 60, and did not have zero as a placeholder. This system was developed around the same time as the Egyptian numeration system.

6) What is the Mayan Numeration Form based on?

Uses base 5-diagonally based-Level 1=1; Level 2=5; Level 3=25; Level 4=125....

Uses base 10-horizontally based-Level 1=1; Level 2=10; Level 3=100; Level 4=1000....

Uses base 30-circumferentially based-Level 1=1; Level 2=30; Level 3=30x30; Level 4=30x30^2....

-uses base 20-vertically based-Level 1=1; Level 2=20; Level 3=18x20; Level 4=18x20^2...

The Mayan Numeration Form is based on base 20, vertically oriented, where each level is calculated by multiplying the previous level by 20. This system is a unique way of representing numbers in the Mayan civilization.

Explanation

The Mayan Numeration Form is based on base 20, vertically oriented, where each level is calculated by multiplying the previous level by 20. This system is a unique way of representing numbers in the Mayan civilization.

7) What is the Roman Numeration Form?

Roman Numeration Form involves adding all numbers in a sequence without any subtraction properties.

-uses base 10- when a number decrease then increases, subtract-number must be in chart to subtract[subtraction property]

Roman Numeration Form relies on base 12 for its calculations and representations.

Roman Numeration Form follows base 5 - all numbers are divisible by 5.

Roman Numeration Form follows a base 10 system where numbers decrease and then increase, indicating the need for subtraction when appropriate.

Explanation

Roman Numeration Form follows a base 10 system where numbers decrease and then increase, indicating the need for subtraction when appropriate.

8) What does Base 5 Numeration Form refer to?

A system where numbers are represented using a mix of base 8 and base 10

Counting using only odd numbers

A method of counting only even numbers

-based on hands a fingers (you have 4 fingers and 1 thumb)[Ex. 21 five--21=hand and five=fingers--is 11]

Base 5 Numeration Form refers to a counting system based on hands and fingers, where each hand represents 5 and each finger represents 1. This allows for counting up to 25 using both hands and fingers.

Explanation

Base 5 Numeration Form refers to a counting system based on hands and fingers, where each hand represents 5 and each finger represents 1. This allows for counting up to 25 using both hands and fingers.

9) How should we convert numbers in different bases to Hindu-Arabic Base 10 numeration form?

Use a calculator to directly convert the number to Base 10.

Ignore all exponents and simply add all the digits of the number together.

Convert all numbers to Roman numerals first, then subtract and add accordingly.

-write out our value in expanded form-multiply all the exponents-add

Converting numbers in different bases to Base 10 requires writing out the value in expanded form, multiplying all the exponents, and then adding them together to get the result in Hindu-Arabic numeration form.

Explanation

Converting numbers in different bases to Base 10 requires writing out the value in expanded form, multiplying all the exponents, and then adding them together to get the result in Hindu-Arabic numeration form.

10) How do you convert a Hindu-Arabic number into different bases?

Subtract the number from the base repeatedly until reaching 0.

-look for greatest exponent less than value-determine how many groups in the value-continue until you reach n* power

Divide the number by the exponent of the base.

Add all the digits of the number together.

Converting Hindu-Arabic numbers to different bases involve identifying the greatest exponent less than the value and determining the number of groups in the value. This process is continued until reaching n*power, representing the conversion into different bases.

Explanation

Converting Hindu-Arabic numbers to different bases involve identifying the greatest exponent less than the value and determining the number of groups in the value. This process is continued until reaching n*power, representing the conversion into different bases.

11) What is the Base 12 numeration form?

In Base 12 numeration form, T represents groups of 7, and E represents groups of 8.

In Base 12 numeration form, T represents groups of 8, and E represents groups of 9.

In Base 12 numeration form, T represents groups of 9, and E represents groups of 10.

-based on dozens (12's)-T is groups of 10-E is groups of 11[Write in expanded form first]

Base 12 numeration form is based on multiples of 12, where T represents 10 because it is one less than a dozen (12), and E represents 11 as the next number before another dozen.

Explanation

Base 12 numeration form is based on multiples of 12, where T represents 10 because it is one less than a dozen (12), and E represents 11 as the next number before another dozen.