4.5.4: Chapter Review

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    Hindu-Arabic Positional System

    Exercise \(\PageIndex{1}\)

    What is the base of \(5^7\) ?

    Exercise \(\PageIndex{2}\)

    What is the exponent of \(5^7\) ?

    Exercise \(\PageIndex{3}\)

    Compute \(4^5+3^2\).

    Exercise \(\PageIndex{4}\)

    Convert the Hindu-Arabic number into expanded form: 4,201.

    Exercise \(\PageIndex{5}\)

    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

    Exercise \(\PageIndex{6}\)

    Which systems—Hindu-Arabic, Roman, Mayan, or Babylonian—are additive systems?

    Exercise \(\PageIndex{7}\)

    Which systems—Hindu-Arabic, Roman, Mayan, or Babylonian—are positional systems?

    Exercise \(\PageIndex{8}\)

    Which systems—Hindu-Arabic, Roman, Mayan, or Babylonian—use a 0?

    Exercise \(\PageIndex{9}\)

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

    Exercise \(\PageIndex{10}\)

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

    Exercise \(\PageIndex{11}\)

    Convert the Babylonian numeral to a Hindu-Arabic numeral.

    Babylonian numeral 8 is displayed. Babylonian numeral 21 is displayed.

    Exercise \(\PageIndex{12}\)

    Convert the Mayan numeral to a Hindu-Arabic numeral.

    Mayan numeral 8 is displayed.

    Mayan numeral 14 is displayed.

    Exercise \(\PageIndex{13}\)

    Convert the Roman numeral MMCDXLVII into a Hindu-Arabic numeral.

    Exercise \(\PageIndex{14}\)

    Convert the Hindu-Arabic numeral 394 to a Roman numeral.

    Converting with Base Systems

    Exercise \(\PageIndex{15}\)

    List the numbers from 0 to 100 in base 5.

    Exercise \(\PageIndex{16}\)

    In base 8, what is the place value of the 3 in the number 6388?

    Exercise \(\PageIndex{17}\)

    How many symbols are needed for a base 17 system?

    Exercise \(\PageIndex{18}\)

    What does it mean for a number to be in base 6?

    Exercise \(\PageIndex{19}\)

    What symbols are used in a base 12 system?

    Exercise \(\PageIndex{20}\)

    When converting from a base 10 number to a base 2 number, would the number of digits decrease?

    Exercise \(\PageIndex{21}\)

    Convert 3115 to base 10.

    Exercise \(\PageIndex{22}\)

    Convert 4512 to base 10.

    Exercise \(\PageIndex{23}\)

    Convert 10012 to base 10.

    Exercise \(\PageIndex{24}\)

    Convert 459 to base 8.

    Exercise \(\PageIndex{25}\)

    Convert 1198 to base 12.

    Exercise \(\PageIndex{26}\)

    Convert 38 to base 2.

    Exercise \(\PageIndex{27}\)

    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

    Exercise \(\PageIndex{28}\)

    Create the addition table for base 5.

    Exercise \(\PageIndex{29}\)

    How many addition rules are there for a base 7 system?

    Exercise \(\PageIndex{30}\)

    Calculate 345 + 445.

    Exercise \(\PageIndex{31}\)

    Calculate A712 + 8812.

    Exercise \(\PageIndex{32}\)

    Calculate 5416 − 2336.

    Exercise \(\PageIndex{33}\)

    Calculate 5B12 − 1A12.

    Exercise \(\PageIndex{34}\)

    When adding in base 8, the result 9118 is found. How do we know a mistake was made?

    Multiplication and Division in Base Systems

    Exercise \(\PageIndex{35}\)

    What is the process for creating the multiplication table for a base other than 10 ?

    Exercise \(\PageIndex{36}\)

    Create the multiplication table for base 7.

    Exercise \(\PageIndex{37}\)

    How many multiplication rules are there in a base 3 system?

    Exercise \(\PageIndex{38}\)

    Calculate \(14_7 \times 25_7\).

    Exercise \(\PageIndex{39}\)

    Calculate \(67_{12} \times 3 B_{12}\).

    Exercise \(\PageIndex{40}\)

    Calculate \(42_7 \div 5_7\).

    Exercise \(\PageIndex{41}\)

    Calculate \(38_{12} \div \mathrm{B}_{12}\).

    Exercise \(\PageIndex{42}\)

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

    This page titled 4.5.4: Chapter Review was last modified on Thu, 02 Jan 2025 09:27:24 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.