Question 1

In what base does the following addition NOT work: 13 + 13 = 26?

Accepted Answer

A)  base six 
B)  base seven 
C)  base eight 
D)  base ten 
E)  It works in all of these bases. 
A)  base six 
B)  base seven 
C)  base eight 
D)  base ten 
E)  It works in all of these bases. A

Question 2

In base ten, 215.687 is exactly _____ ones, exactly _____ tens, exactly _____ hundreds, and exactly _____ thousands; also, 3421 is exactly _____ tenths and exactly _____ hundredths.

Accepted Answer

215.687; 21.5687; 2.15687; 0.215687; 34210; 342100

Question 3

The base-ten fraction 1/4 equals which base-eight numeral?

Accepted Answer

A)  0.2eight 
B)  0.14eight 
C)  0.02eight 
D)  1.4eight 
A)  0.2eight 
B)  0.14eight 
C)  0.02eight 
D)  1.4eight A

Question 4

Write an addition equation for (# fingers) + (# toes) = (answer) in some base other than base ten.

Accepted Answer

The answer of Write an addition equation for (# fingers)...

Question 5

632.1 has 632.1 ones in it.

Accepted Answer

A) True 
 B)False

Question 6

In base b, there are b - 1 different digits.

Accepted Answer

A) True 
 B)False

Question 7

If you have been counting in base five, what would have been the five numerals BEFORE 2314five?

Accepted Answer

Question 8

The base b numeral 321b means:

Accepted Answer

A)  3 . b2 + 2 . b1 + 1. 
B)  3 . b3 + 2 . b2 + 1 . b1. 
C)  6b. 
D)  3 . b + 2 . b + 1. 
A)  3 . b2 + 2 . b1 + 1. 
B)  3 . b3 + 2 . b2 + 1 . b1. 
C)  6b. 
D)  3 . b + 2 . b + 1.

Question 9

The base-four numeral 11.1four could be written in base ten as:

Accepted Answer

A)  $33 \frac { 1 } { 4 }$ 
B)  $33 \frac { 1 } { 10 }$ 
C)  $11 \frac { 1 } { 4 }$ 
D) 5 $\frac { 1 } { 4 }$ 
A)  $33 \frac { 1 } { 4 }$ 
B)  $33 \frac { 1 } { 10 }$ 
C)  $11 \frac { 1 } { 4 }$ 
D) 5 $\frac { 1 } { 4 }$

Question 10

How many tenths are in 1.03? How many whole tenths?

Accepted Answer

The answer of How many tenths are in 1.03? How...

Question 11

Below is a partially completed addition, written in connection with base five pieces. At the time of the work below, what base pieces would be displayed if the small piece were the unit? (Drawings or word descriptions are okay.)
Finish the numerical calculation. (You do not have to draw the base pieces for the rest of the work.)

? $ \begin{array}{r}1 \ 214 \text { five } \ +\underline{33} \text { five } \ 2\end{array} $

Accepted Answer

There would be two flats, five

Question 12

A place-value, base-twenty system would require _____ digits.

Accepted Answer

The answer of A place-value, base-twenty system would require _____...

Question 13

Is the old Greek numeration system ( $?$ = 1, $\beta$  = 2, $y$  = 3, etc.) a place-value system? Explain.

Accepted Answer

No. A place-value system requi

Question 14

Most present-day societies use the Hindu-Arabic numeration system.

Accepted Answer

A) True 
 B)False

Question 15

34.597 has 345 whole tenths in it.

Accepted Answer

A) True 
 B)False

Question 16

Use drawings of multibase blocks to illustrate 32five + 23five.

Accepted Answer

@#IMG-DLM& 
The five small squares can b

Question 17

Suppose you visited an alien planet and the creatures wrote numbers in order as follows: "obi, fin, mus, obi-na, obi-obi, obi-fin, obi-mus…" These creatures must be using which base?

Accepted Answer

A)  base ten 
B)  base three 
C)  base four 
D)  base nine 
E)  base twelve 
A)  base ten 
B)  base three 
C)  base four 
D)  base nine 
E)  base twelve

Question 18

In base b, 3 + 2b3 + b would be written _____.

Accepted Answer

Question 19

1ten = _____twelve.

Accepted Answer

Question 20

How many $100 bills would make $45 billion?

Accepted Answer

The answer of How many $100 bills would make $45...

Exam 2: Numeration Systems

In what base does the following addition NOT work: 13 + 13 = 26?

In base ten, 215.687 is exactly _____ ones, exactly _____ tens, exactly _____ hundreds, and exactly _____ thousands; also, 3421 is exactly _____ tenths and exactly _____ hundredths.

The base-ten fraction 1/4 equals which base-eight numeral?

Write an addition equation for (# fingers) + (# toes) = (answer) in some base other than base ten.

632.1 has 632.1 ones in it.

In base b, there are b - 1 different digits.

If you have been counting in base five, what would have been the five numerals BEFORE 2314five?

The base b numeral 321b means:

The base-four numeral 11.1four could be written in base ten as:

How many tenths are in 1.03? How many whole tenths?

A place-value, base-twenty system would require _____ digits.

Is the old Greek numeration system ( ??? = 1, β\betaβ = 2, yyy = 3, etc.) a place-value system? Explain.

Most present-day societies use the Hindu-Arabic numeration system.

34.597 has 345 whole tenths in it.

Use drawings of multibase blocks to illustrate 32five + 23five.

Suppose you visited an alien planet and the creatures wrote numbers in order as follows: "obi, fin, mus, obi-na, obi-obi, obi-fin, obi-mus…" These creatures must be using which base?

In base b, 3 + 2b3 + b would be written _____.

1ten = _____twelve.

How many $100 bills would make $45 billion?

Reasoning About Quantities

Understanding Whole Number Operations

Some Conventional Ways of Computing

Using Numbers in Sensible Ways

Meanings for Fractions

Computing With Fractions

Multiplicative Comparisons and Multiplicative Reasoning

Ratios, Rates, Proportions, and Percents

Integers and Other Number Systems

Number Theory

What Is Algebra

A Quantitative Approach to Algebra and Graphing

Understanding Change: Relationships Among Time, Distance, and Rate

Further Topics in Algebra and Change

Polygons

Polyhedra

Symmetry

Tessellations

Similarity

Curves, Constructions, and Curved Surfaces

Transformation Geometry

Measurement Basics

Area, Surface Area, and Volume

Counting Units Fast: Measurement Formulas

Special Topics in Measurement

Quantifying Uncertainty

Determining More Complicated Probabilities

Introduction to Statistics and Sampling

Representing and Interpreting Data With One Variable

Dealing With Multiple Data Sets or With Multiple Variables

Variability in Samples

Special Topics in Probability

Filters

In base ten, 215.687 is exactly ___ ones, exactly _ tens, exactly _ hundreds, and exactly _ thousands; also, 3421 is exactly _ tenths and exactly ___ hundredths.

If you have been counting in base five, what would have been the five numerals BEFORE 2314_five?

The base b numeral 321_b means:

The base-four numeral 11.1_four could be written in base ten as:

Is the old Greek numeration system ( $?$ = 1, $\beta$ = 2, $y$ = 3, etc.) a place-value system? Explain.

Use drawings of multibase blocks to illustrate 32_five + 23_five.

In base b, 3 + 2b³ + b would be written _____.

1_ten = ______twelve.