1.3: Topic C Place Value
 Page ID
 95390
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left#1\right}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Topic C: Place Value
As you know, we count much higher than ten in our world. Each place in a number has a value.
The ones place tells how many ones there are.
 3 means 3 ones. \(\square \square \square\)
 0 means 0 ones
 9 means 9 ones \(\square \square \square \square \\ \square \square \square \square \square\)
9 is the largest amount that we can express (write or say) with one digit.
The tens place shows how many tens there are. The ones place must have a digit in it before there can be a digit in the tens place.
Every ten is ten ones.
43 means 4 tens and 3 ones.
20 means 2 tens and 0 ones. The zero holds the ones place.
99 means 9 tens and 9 ones. 99 is the largest amount that we can express (write or say) using only two digits.
Exercise 1
Fill in the blanks to make each sentence true. Draw a picture for questions c, f, h, and j like the examples. Check your work using the answer key at the end of the exercise. Ask your instructor to check your sketches.
Example
49 means 4 tens and 9 ones.
 37 means _____ tens and _____ ones.
 65 means _____ tens and _____ ones.
 56 means _____ tens and _____ ones.
 87 means _____ tens and _____ ones
 33 means _____ tens and _____ ones.
 60 means _____ tens and _____ ones.
Answers to Exercise 1
 3 tens, 7 ones
 6 tens, 5 ones
 5 tens, 6 ones
 8 tens, 7 ones
 3 tens, 3 ones
 6 tens, 0 ones
The place to the left of the tens place is the hundreds place. It shows how many hundreds there are. A number written using three whole digits has a hundreds place, a tens place, and a ones place.
Every hundred is the same as ten tens, and every hundred is the same as one hundred ones.
Every hundred is ten tens – every hundred is the same as one hundred ones.
100 100 100
425 means 4 hundreds, 2 tens, and 5 ones
354 means 3 hundreds, 5 tens, and 4 ones
Exercise 2
Fill in the blanks to make each sentence true. Draw a picture for questions b, c, d, and e, like the examples. Check your work using the answer key at the end of the exercise. Ask your instructor to check your sketches.
 190 = 1 hundreds, 9 tens, 0 ones.
 555 = _____ hundreds, _____ tens, _____ ones.
 309 = _____ hundreds, _____ tens, _____ ones.
 499 = _____ hundreds, _____ tens, _____ ones.
 480 = _____ hundreds, _____ tens, _____ ones.
Answers to Exercise 2
 5 hundreds, 5 tines, 5 ones
 3 hundreds, 0 tens, 9 ones
 4 hundreds, 9 tens, 9 ones
 4 hundreds, 8 tens, 0 ones
Exercise 3
Count the hundreds, tens, and ones shown in the drawings. The pictures will help you understand the quantity of a number. Then write the numeral. The first one is done for you. Check your work using the answer key at the end of the exercise.
 2 hundreds, 0 tens, 3 ones = 203
 hundreds, tens, ones =
 hundreds, tens, ones =
 hundreds, tens, ones =
Answers to Exercise 3
 4 hundreds, 3 tens, 1 ones
 1 hundreds, 8 tens, 0 ones
 2 hundreds, 0 tens, 3 ones
Need more practice?
Ask your instructor for some fake money. Using the one, ten, and hundred dollar bills, practice trading ten of one type of bill for one of the next value.
Exercise 4
Write the place value name (ones, tens, hundreds) for each underlined digit. Check your work using the answer key at the end of the exercise.
 622 hundreds
 468 tens
 920
 920
 648
 426
 534
 555
 451
 901
 226
 486
Answers to Exercise 4
 ones
 hundreds
 tens
 ones
 hundreds
 tens
 tens
 ones
 hundreds
 ones
Exercise 5
Underline the digit for the place value named. Check your work using the answer key at the end of the exercise.
 hundreds, 416
 tens, 368
 tens, 364
 hundreds, 456
 ones, 206
 ones, 634
Answers to Exercise 5
 4
 6
 6
 4
 6
 4
Emotions Check
How are you feeling?
 Are your palms moist?
 How is your breathing?
Take control. Be the boss. If you are feeling anxious, practice your breathing exercise.
Remember: Breathe in slowly to the count of four, hold it for the count of four.
Reading and Writing Numerals
You know that the digits are 0 1 2 3 4 5 6 7 8 9 and that digits are arranged in different places so we can count larger amounts than our ten fingers!
When we use digits, we call what we write the numeral.
 328 is a numeral
 46 is a numeral
 3 is a numeral
We use numerals to represent numbers.
If we think about language instead of mathematics it will be clearer.
Letters are used to make words. We respond to the meaning of words.
 Digits are the “letters” of math.
 Numerals are the “words” of math.
 Numbers are the “meaning” of math.
Now you know the place value of digits up to three places. Next you will learn to read and write numerals and number words. Some of the words to read and spell may be new to you.
The numerals from 1 to 12 have special words. These are:
Numeral  Word Name 

0  zero 
1  one 
2  two 
3  three 
4  four 
5  five 
6  six 
7  seven 
8  eight 
9  nine 
10  ten 
11  eleven 
12  twelve 
The number names for numerals from 13 to 19 are made up of two parts. The first part tells us how many units. The second part (“teen”) tells us there is also 1 ten.
Numeral  Word Name  Meaning 

13  thirteen  three units and 1 ten 
14  fourteen  four units and 1 ten 
15  fifteen  five units and 1 ten 
16  sixteen  six units and 1 ten 
17  seventeen  seven units and 1 ten 
18  eighteen  eight units and 1 ten 
19  nineteen  nine units and 1 ten 
Exercise 6
Write the word name for each number. Try not to look at the list. Check your work using the answer key at the end of the exercise.
 6
 17
 4
 14
 12
 13
Answers to Exercise 6
 six
 seventeen
 four
 fourteen
 twelve
 thirteen
The word names for the numbers 20 to 90 are also made up of two parts. The first part tells us how many groups of tens. The second part (“ty”) tells us we are counting groups of tens and not something else. The “ty” may have come from a shortening of the word “ten”.
Number  Word Name  Meaning 

20  twenty  two tens 
30  thirty  three tens 
40  forty  four tens 
50  fifty  five tens 
60  sixty  six tens 
70  seventy  seven tens 
80  eighty  eight tens 
90  ninety  nine tens 
The names for the numbers between groups of tens also follow a pattern. The first number tells us how many tens. The second number tells us how many ones.
Tens Ones  Tens Ones  Tens Ones 

20 twenty  30 thirty  40 forty 
21 twentyone  31 thirtyone  41 fortyone 
22 twentytwo  32 thirtytwo  42 fortytwo 
23 twentythree  33 thirtythree  43 fortythree 
24 twentyfour  34 thirtyfour  44 fortyfour 
25 twentyfive  35 thirtyfive  45 fortyfive 
26 twentysix  36 thirtysix  46 fortysix 
27 twentyseven  37 thirtyseven  47 fortyseven 
28 twentyeight  38 thirtyeight  48 fortyeight 
29 twentynine  39 thirtynine  49 fortynine 
The written names for numbers that have tens and ones are written with a hyphen () between them. This pattern with the hyphen continues up to ninetynine (99).
Exercise 7
Write the word names for these numbers. Check your work using the answer key at the end of the exercise.
 24 twentyfour
 35 thirtyfive
 83 _____
 46 _____
 59 _____
 20 _____
 53 _____
 25 _____
 15 _____
 38 _____
Answers to Exercise 7
 eightythree
 fortysix
 fiftynine
 twenty
 fiftythree
 twentyfive
 fifteen
 thirtyeight
Exercise 8
Write the numerals for these word names. Check your work using the answer key at the end of the exercise.
 ninetynine 99
 sixtyseven 67
 eightyone _____
 eighteen _____
 twentysix _____
 thirteen _____
 thirty _____
 fortythree _____
Answers to Exercise 8
 81
 18
 26
 13
 30
 43
When we write hundreds in words, we need two words. The first word tells us how many hundreds. The second word tells us we are counting hundreds.
200 two hundred
You now know how to write numbers in words up to 999.
Remember
 hyphen () between the tens and units
 no hyphen anywhere else
 no “s” on the hundred
 no “and” between the hundreds place and the tens place
\[\begin{array}{llll} \mathbf{367 } \text{ is made of:} & \mathbf{3} \text{ hundreds} & \mathbf{6} \text{ tens} & \mathbf{7} \text{ ones} \\ \text{Each is written:}& \text{three hundred} & \text{sixty} & \text{seven}\end{array} \\ \text{Put the parts together: } \textbf{three hundred sixtyseven}\]
Here is another example. Watch out for the empty space!
\[\begin{array}{llll} \mathbf{504 } \text{ is made of:} & \mathbf{5} \text{ hundreds} & \mathbf{0} \text{ tens} & \mathbf{4} \text{ ones} \\ \text{Each is written:}& \text{fice hundred} & & \text{four}\end{array} \\ \text{Put the parts together: } \textbf{five hundred four}\]
Here is another example. Watch out for the empty space!
\[\begin{array}{llll} \mathbf{890} \text{ is made of:} & \mathbf{8} \text{ hundreds} & \mathbf{9} \text{ tens} & \mathbf{0} \text{ ones} \\ \text{Each is written:}& \text{eight hundred} & \text{ninety} & \end{array} \\ \text{Put the parts together: } \textbf{eight hundred ninety}\]
Here is another example. Watch out for the empty space!
\[\begin{array}{llll} \mathbf{100} \text{ is made of:} & \mathbf{1} \text{ hundreds} & \mathbf{0} \text{ tens} & \mathbf{0} \text{ ones} \\ \text{Each is written:}& \text{one hundred} & & \end{array} \\ \text{Put the parts together: } \textbf{one hundred}\]
Remember
Empty spaces are not written in words.
Exercise 9
Write the word names for these numerals. Check your work using the answer key at the end of the exercise.
 623 is made of: _____
Each is written: _____
Put the parts together: _____  364 is made of: _____
Each is written: _____
Put the parts together: _____  213 is made of: _____
Each is written: _____
Put the parts together: _____  405 is made of: _____
Each is written: _____
Put the parts together: _____
Now, write the word name for each number. Check your work using the answer key at the end of the exercise.
 704
 470
 993
 100
 972
Answers to Exercise 9
 623 is made of: 6 hundreds, 2 tens, 3 ones
Each is written: six hundred, twenty, three
Put the parts together: six hundred twentythree  364 is made of:3 hundreds, 6 tens, 4 ones
Each is written: three hundred, sixty, four
Put the parts together: three hundred sixtyfour  213 is made of: 2 hundreds. 1 ten, 3 ones
Each is written: two hundred, thirteen
Put the parts together: two hundred thirteen  405 is made of:4 hundreds, 0 tens, 5 ones
Each is written: four hundred, five
Put the parts together: four hundred five  seven hundred four
 four hundred seventy
 nine hundred ninetythree
 one hundred
 nine hundred seventytwo
Topic C SelfTest
Mark /17 Aim 14/17
 Write the place value for the underlined digit. (6 marks)
 765
 903
 479
 185
 732
 397
 Write the word names for these numerals. (6 marks)
 79
 492
 378
 820
 405
 583
 Write the numerals for these word names. (5 marks)
 five hundred fortyseven
 three hundred eighty
 two hundred seventyfive
 four hundred sixteen
 nine hundred twentythree
Answers to Topic C SelfTest

 tens
 tens
 hundreds
 ones
 ones
 hundreds

 seventynine
 four hundred ninetytwo
 three hundred seventyeight
 eight hundred twenty
 four hundred five
 five hundred eightythree

 547
 380
 275
 416
 923