Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Textbook Question
Chapter 4.1, Problem 59E
The ancient Egyptian system described in this section was simple grouping, used a base of ten, and contained seven distinct symbols. The largest number expressible in that system is 9,999,999. Identify the largest number expressible in each of the following simple grouping systems. (In Exercises 61 -64, d can be any counting number.)
base five, five distinct symbols
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Recall that the ancient Egyptian system described in this section was simple grouping, used a base of ten, and
contained seven distinct symbols. The largest number expressible in that system is 9,999,999. Identify the largest
number expressible in the following simple grouping system.
base ten, 5 distinct symbols
The largest number expressible would be
(Type a whole number.)
We usually write numbers in decimal form (or base 10), meaning numbers are composed using
10 different “digits" {0, 1, ... , 9}. Sometimes though it is useful to write numbers hexadecimal
or base 16. Now there are 16 distinct digits that can be used to form numbers:
{0, 1, ...,9, A, B, C, D, E, F}. So for example, a 3 digit hexadecimal number might be 2B8.
Assume that digits and letter can be repeated.
a. How many 6-digit hexadecimals are there in which the first digit is E or F?
b. How many 3-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)?
c. How many 4-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or
both)?
We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10
different “digits" {0, 1, ...,9}. Sometimes though it is useful to write numbers hexadecimal or base
16. Now there are 16 distinct digits that can be used to form numbers:
{0, 1,...,9, A, B, C,D, E, F}. So for example, a 3 digit hexadecimal number might be 2B8. Assume
that digits and letter can be repeated.
a. How many 4-digit hexadecimals are there in which the first digit is E or F?
b. How many 3-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)?
c. How many 5-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or
both)?
Chapter 4 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 4.1 - Convert each Egyptian numeral to Hindu-Arabic...Ch. 4.1 - Convert each Egyptian numeral to Hindu-Arabic...Ch. 4.1 - Prob. 3ECh. 4.1 - Convert each Egyptian numeral to Hindu-Arabic...Ch. 4.1 - Convert each Hindu-Arabic numeral to Egyptian...Ch. 4.1 - Convert each Hindu-Arabic numeral to Egyptian...Ch. 4.1 - Convert each Hindu-Arabic numeral to Egyptian...Ch. 4.1 - Convert each Hindu-Arabic numeral to Egyptian...Ch. 4.1 - Chapter Z of the hook of Numbers in the Bible...Ch. 4.1 - Prob. 10E
Ch. 4.1 - Chapter 1 of the hook of Numbers in the Bible...Ch. 4.1 - Prob. 12ECh. 4.1 - Chapter 1 of the hook of Numbers in the Bible...Ch. 4.1 - Chapter 1 of the hook of Numbers in the Bible...Ch. 4.1 - Convert each Roman numeral to Hindu-Arabic form....Ch. 4.1 - Convert each Roman numeral to Hindu-Arabic...Ch. 4.1 - Convert each Roman numeral to Hindu-Arabic form....Ch. 4.1 - Convert each Roman numeral to Hindu-Arabic form....Ch. 4.1 - Convert each Hindu-Arabic numeral to Roman form....Ch. 4.1 - Prob. 20ECh. 4.1 - Convert each Hindu-Arabic numeral to Roman...Ch. 4.1 - Convert each Hindu-Arabic numeral to Roman form....Ch. 4.1 - Convert each Chinese numeral to Hindu-Arabic form.Ch. 4.1 - Convert each Chinese numeral to Hindu-Arabic...Ch. 4.1 - Convert each Chinese numeral to Hindu-Arabic form.Ch. 4.1 - Prob. 26ECh. 4.1 - Convert each Hindu-Arabic numeral to Chinese...Ch. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Convert each Hindu-Arabic numeral to Chinese...Ch. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Work each addition or subtraction problem, using...Ch. 4.1 - Prob. 36ECh. 4.1 - Work each addition or subtraction problem, using...Ch. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Work each addition or subtraction problem, using...Ch. 4.1 - Work each addition or subtraction problem, using...Ch. 4.1 - Work each addition or subtraction problem, using...Ch. 4.1 - Work each addition or subtraction problem, using...Ch. 4.1 - Work each addition or subtraction problem, using...Ch. 4.1 - Work each addition or subtraction problem, using...Ch. 4.1 - Prob. 47ECh. 4.1 - Use the Egyptian algorithm to find each...Ch. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - In Exercises 51 and 52, convert all numbers to...Ch. 4.1 - In Exercises 51 and 52, convert all numbers to...Ch. 4.1 - Explain why each step would be an improvement in...Ch. 4.1 - Explain why each step would be an improvement in...Ch. 4.1 - Explain why each step would be an improvement in...Ch. 4.1 - Prob. 56ECh. 4.1 - The ancient Egyptian system described in this...Ch. 4.1 - Prob. 58ECh. 4.1 - The ancient Egyptian system described in this...Ch. 4.1 - Prob. 60ECh. 4.1 - The ancient Egyptian system described in this...Ch. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - The ancient Egyptian system described in this...Ch. 4.1 - The ancient Egyptian system described in this...Ch. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Prob. 2ECh. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Identify each numeral in Exercises 1-20 as...Ch. 4.2 - Prob. 21ECh. 4.2 - Write each number as a Babylonian numeral. 32Ch. 4.2 - Write each number as a Babylonian numeral.
23....Ch. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Write each number as a Babylonian numeral. 3280Ch. 4.2 - Write each number as a Babylonian numeral.
27....Ch. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Write each number as a Mayan numeral. 4694Ch. 4.2 - Write each number as a Mayan numeral. 4328Ch. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Prob. 55ECh. 4.2 - Write each number as a Greek numeral.Ch. 4.3 - Write each number in expanded form. 73Ch. 4.3 - Write each number in expanded form. 265Ch. 4.3 - Write each number in expanded form
3. 8335
Ch. 4.3 - Write each number in expanded form 12,398Ch. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Perform each subtraction using the nines...Ch. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - Identify the number represented on each...Ch. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Sketch an abacus to show each number.
36. 183
Ch. 4.3 - 2547 Sketch an abacus to show each number.Ch. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Use the lattice method to find each product. 32741Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Refer to Example 10 where Napier's rods were used....Ch. 4.3 - Prob. 45ECh. 4.3 - Use Napier's rods (Figure 9) to find each product....Ch. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Use the Russian peasant method to find each...Ch. 4.3 - Prob. 53ECh. 4.3 - The Hindu-Arabic system is positional and uses ten...Ch. 4.4 - List the first twenty counting numbers in each...Ch. 4.4 - List the first twenty counting numbers in each...Ch. 4.4 - List the first twenty counting numbers in each...Ch. 4.4 - List the first twenty counting numbers in each...Ch. 4.4 - Write (in the same base) the counting numbers just...Ch. 4.4 - Write (in the same base) the counting numbers just...Ch. 4.4 - Write (in the same base) the counting numbers just...Ch. 4.4 - Write (in the same base) the counting numbers just...Ch. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Determine, in each base, the least and greatest...Ch. 4.4 - Determine, in each base, the least and greatest...Ch. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Convert each number to decimal form by expanding...Ch. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Convert each number from decimal form to the given...Ch. 4.4 - Convert each number from decimal form to the given...Ch. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Make each conversion as indicated. 6748nine to...Ch. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Convert each number from octal form to binary...Ch. 4.4 - Convert each number from binary form to octal...Ch. 4.4 - Convert each number from binary form to octal...Ch. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Make each conversion as indicated.
45. 101101two...Ch. 4.4 - Make each conversion as indicated.
46....Ch. 4.4 - Identify the greatest number from each list.
47.
Ch. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - There is a theory that twelve would be a better...Ch. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Break each code into groups of seven digits and...Ch. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - If the IP address and subnet mask for a computer...Ch. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Prob. 66ECh. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Prob. 73ECh. 4.4 - In our decimal system, we distinguish odd and even...Ch. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.4 - Determine whether the given base-five numeral...Ch. 4.4 - Prob. 80ECh. 4.4 - Prob. 81ECh. 4.4 - Determine whether the given base-five numeral...Ch. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4.4 - Prob. 88ECh. 4.4 - Prob. 89ECh. 4.4 - Prob. 90ECh. 4.4 - Prob. 91ECh. 4.4 - Prob. 92ECh. 4.4 - Prob. 93ECh. 4.4 - Prob. 94ECh. 4.4 - Prob. 95ECh. 4.4 - Prob. 96ECh. 4 - In each case, identify the numeration system, and...Ch. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - Perform each operation using the alternative...Ch. 4 - Perform each operation using the alternative...Ch. 4 - Prob. 9TCh. 4 - Convert each number to base ten. 243fiveCh. 4 - Prob. 11TCh. 4 - Prob. 12TCh. 4 - Prob. 13TCh. 4 - Prob. 14TCh. 4 - Prob. 15TCh. 4 - Prob. 16TCh. 4 - Prob. 17TCh. 4 - Prob. 18TCh. 4 - Prob. 19TCh. 4 - Prob. 20TCh. 4 - Briefly explain each of the following. the...Ch. 4 - Briefly explain each of the following.
22 the...Ch. 4 - Prob. 23TCh. 4 - Briefly explain each of the following. Illustrate...
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