Chapter 4

Write each Hindu-Arabic numeral as a Roman numeral. 1896

Multiply in the indicated base. $$ \begin{array}{r} 21_{\text {four }} \\ \times 12_{\text {four }} \\ \hline \end{array} $$

Convert each base ten numeral to a numeral in the given base. 87 to base five

Write each Hindu-Arabic numeral as a Roman numeral. 4578

Multiply in the indicated base. $$ \begin{array}{r} 32_{\text {four }} \\ \times 23_{\text {four }} \\ \hline \end{array} $$

Convert each base ten numeral to a numeral in the given base. 85 to base seven

Write each Hindu-Arabic numeral as a Roman numeral. 6892

Use the multiplication tables shown below to divide in the indicated base. \(2 _ { \text { four } } \longdiv { 1 0 0 _ { \text { four } } }\)

Convert each base ten numeral to a numeral in the given base. 108 to base four

Write each Hindu-Arabic numeral as a Roman numeral. 5847

Convert each base ten numeral to a numeral in the given base. 199 to base four

Use the multiplication tables shown below to divide in the indicated base. \(3 _ { \text { five } } \longdiv { 2 2 4 _ { \text { five } } }\)

Convert each base ten numeral to a numeral in the given base. 19 to base two

Convert each base ten numeral to a numeral in the given base. 23 to base two

Perform the indicated operations. \(10110_{\text {two }}+10100_{\text {two }}+11100_{\text {two }}\)

Convert each base ten numeral to a numeral in the given base. 57 to base two

Perform the indicated operations. \(11100_{\text {two }}+11111_{\text {two }}+10111_{\text {two }}\)

Convert each base ten numeral to a numeral in the given base. 63 to base two

Perform the indicated operations. \(11111_{\text {two }}+10110_{\text {two }}-101_{\text {two }}\)

Convert each base ten numeral to a numeral in the given base. 90 to base two

Perform the indicated operations. \(10111_{\text {two }}+11110_{\text {two }}-111_{\text {two }}\)

Convert each base ten numeral to a numeral in the given base. 87 to base two

Write each Hindu-Arabic numeral as a traditional Chinese numeral. 43

Perform the indicated operations. \(1011_{\text {two }} \times 101_{\text {two }}\)

Convert each base ten numeral to a numeral in the given base. 138 to base three

Write each Hindu-Arabic numeral as a traditional Chinese numeral. 269

Perform the indicated operations. \(1101_{\text {two }} \times 110_{\text {two }}\)

Convert each base ten numeral to a numeral in the given base. 129 to base three

Write each Hindu-Arabic numeral as a traditional Chinese numeral. 583

Perform the indicated operations. \(\mathrm{D} 3_{\text {sixteen }} \times 8 \mathrm{~A}_{\text {sixteen }}\)

Convert each base ten numeral to a numeral in the given base. 386 to base six

Write each Hindu-Arabic numeral as a traditional Chinese numeral. 2965

Perform the indicated operations. \(\mathrm{B} 5_{\text {sixteen }} \times 2 \mathrm{C}_{\text {sixteen }}\)

Convert each base ten numeral to a numeral in the given base. 428 to base nine

Write each Hindu-Arabic numeral as a traditional Chinese numeral. 4870

Convert each base ten numeral to a numeral in the given base. 1599 to base seven

Write each Hindu-Arabic numeral as a traditional Chinese numeral. 7605

Convert each base ten numeral to a numeral in the given base. 1346 to base eight

Write each Ionic Greek numeral as a Hindu-Arabic numeral. \(\iota \beta\)

Describe how to add two numbers in a base other than ten. How do you express and record the sum of numbers in a column if that sum exceeds the base?

Describe how to subtract two numbers in a base other than ten. How do you subtract a larger number from a smaller number in the same column?

Describe two difficulties that youngsters encounter when learning to add, subtract, multiply, and divide using HinduArabic numerals. Base your answer on difficulties that are encountered when performing these computations in bases other than ten.

Performing the following addition problem reminds me of adding in base sixty. 4 hours, 26 minutes, 57 seconds \(+3\) hours, 46 minutes, 39 seconds

Performing the following subtraction problem reminds me of subtracting in base sixty. 8 hours, 45 minutes, 28 seconds \(-2\) hours, 47 minutes, 53 seconds

Write the binary representation for each letter. \(\mathbf{Y}\)

Group members should research various methods that societies have used to perform computations. Include finger multiplication, the galley method (sometimes called the Gelosia method), Egyptian duplation, subtraction by complements, Napier's bones, and other methods of interest in your presentation to the entire class.

Break each binary sequence into groups of seven digits and write the word represented by the sequence. 101000010000011001100

Express each expanded form as a Hindu-Arabic numeral. \(\left(4 \times 10^{-1}\right)+\left(7 \times 10^{-2}\right)+\left(5 \times 10^{-3}\right)+\left(9 \times 10^{-4}\right)\)

Organize a debate. One side represents people who favor performing computations by hand, using the methods and procedures discussed in this section, but applied to base ten numerals. The other side represents people who favor the use of calculators for performing all computations. Include the merits of each approach in the debate.

Break each binary sequence into groups of seven digits and write the word represented by the sequence. 1001100101010110000111001011