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Chapter 4: Problem 71

Describe how to change a base ten numeral to a numeral in another base.

Short Answer

Expert verified
The process of changing a base 10 numeral to another base involves a repetitive process of division by the target base and recording of the remainders. Once the process is complete, the remainders, written in reverse order, form the numeral in the new base.

Step by step solution

01

Identify the Target Base

Determine the base that you want to convert the base 10 numeral to. This base will be used in the subsequent calculations.
02

Start the Division Process

Divide the base 10 numeral by the target base. Be sure to use integer division and keep track of the remainder. The remainder should always be less than the base, if it's not, ensure accuracy of your calculation.
03

Include Remainder

Record the remainder. This is the least significant digit (rightmost digit) in the new base numeral.
04

Repeat Process

Continue this process with each quotient, recording the remainders each time. Repeat until the quotient is equal to zero.
05

Arrange the Remainders

Once the quotient has reached zero, take the list of remainders and arrange them in reverse order, starting from the final remainder obtained, this will give you the numeral in the new base.

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Most popular questions from this chapter

In Exercises 13鈥�24, subtract in the indicated base. $$ \begin{array}{r} 21_{\text {four }} \\ -12_{\text {four }} \\ \hline \end{array} $$

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.

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?

In Exercises 25鈥�34, multiply in the indicated base. $$ \begin{array}{r} 243_{\text {nine }} \\ \times \quad 6 \quad 6 \\ \hline \end{array} $$

In Exercises 25鈥�34, multiply in the indicated base. $$ \begin{array}{r} 543_{\mathrm{six}} \\ \times \quad 5 \mathrm{six} \\ \hline \end{array} $$
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