4.7.5: Chapter Review

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Chapter Review

Hindu-Arabic Positional System

What is the base of 5⁷?

What is the exponent of 5⁷?

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?

10.

In the Mayan system, what are the place values based on?

11.

Convert the Babylonian numeral to a Hindu-Arabic numeral.
$Babylonian numeral 8 is displayed.$ $Babylonian numeral 21 is displayed.$

12.

Convert the Mayan numeral to a Hindu-Arabic numeral.
$Mayan numeral 8 is displayed.$
$Mayan numeral 14 is displayed.$

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 + 88_12.

32.

Calculate 541₆ − 233_6.

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

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40.

Calculate /**/{42_7} \div {5_7}/**/.

41.

Calculate /**/{38_{12}} \div

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/**/.

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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Chapter Review

Hindu-Arabic Positional System