Unit 1: Number Sense
Topic A: Place Value
Introduction to Place Values
Each place in a number has a value.
Ones
The ones place tells how many ones there are.
3 means 3 ones.
9 is the largest amount that we can express (write or say) with one digit.
Tens
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
99 means 9 tens and 9 ones. 99 is the largest amount that we can express (write or say) using only two digits.
Hundreds
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 ten tens – 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.
Thousands
The place to the left of the hundreds place is the thousands place.
One thousand is the same as ten hundreds.
One thousand is the same as one hundred tens.
One thousand is the same as one thousand ones. (You will have to imagine the picture of the one thousand ones!)
Thousands Separator: Use a Space
When we write numerals, a little space is left between the thousands place and the hundreds place. The space makes it easier to read large numerals.
4392 8253 23693
Large numerals used to be written with a comma (,) instead of a space and you may still see numerals like this:
4,392 8,253 23,693
Learn to use the space instead of a comma because that is the preferred style.
Example A
2 212 means 2 thousands, 2 hundreds, 1 ten, and 2 ones
3 064 means 3 thousands, 0 hundreds, 6 tens, and 4 ones
What happens if the 0 is not written to hold the hundreds place? The numerals would then be 364 which stands for the number 3 hundreds, 6 tens, and 4 ones.
364 is not the same as 3 064.
Exercise One
Fill in the blanks to make each sentence true. Draw a sketch if you wish. Check your work using the answer key at the end of the exercise.
 8261 = thousands hundreds tens ones
 4005 = thousands hundreds tens ones
 2931 = thousands hundreds tens ones
 1034 = thousands hundreds tens ones
 2608 = thousands hundreds tens ones
 7543 = thousands hundreds tens ones
 2900 = thousands hundreds tens ones
Answers to Exercise One
 8 thousands 2 hundreds 6 tens 1 ones
 4 thousands 0 hundreds 0 tens 5 ones
 2 thousands 9 hundreds 3 tens 1 ones
 1 thousands 0 hundreds 3 tens 4 ones
 2 thousands 6 hundreds 0 tens 8 ones
 7 thousands 5 hundreds 4 tens 3 ones
 2 thousands 9 hundreds 0 tens 0 ones
Ten thousands
The place value to the left of thousands is ten thousands. As you can tell by the name, one ten thousand is ten thousands. You are not going to get a sketch of these large place values because the page isn’t big enough!
Example B
43692 = 4 ten thousands, 3 thousands, 6 hundreds, 9 tens, and 2 ones
43692 can also be thought of as 43 thousands, 6 hundreds, 9 tens, and 2 ones.
Exercise Two
Fill in the blanks. Check your work using the answer key at the end of the exercise.
ten thousands  thousands  hundreds  tens  ones  

80300  8  0  3  0  0 
OR  80  3  0  0 

ten thousands thousands hundreds tens ones 36981 OR 
ten thousands thousands hundreds tens ones 31205 OR 
ten thousands thousands hundreds tens ones 99999 OR 
ten thousands thousands hundreds tens ones 15002 OR 
ten thousands thousands hundreds tens ones 75125 OR
Answers to Exercise Two

ten thousands thousands hundreds tens ones 36981 3 6 9 8 1 OR 36 9 8 1 
ten thousands thousands hundreds tens ones 31205 3 1 2 0 5 OR 31 2 0 5 
ten thousands thousands hundreds tens ones 99999 9 9 9 9 9 OR 99 9 9 9 
ten thousands thousands hundreds tens ones 15002 1 5 0 0 2 OR 15 0 0 2 
ten thousands thousands hundreds tens ones 75125 7 5 1 2 5 OR 75 1 2 5
Hundred thousands
Have you heard the expression, “They have a 6 figure salary.” That means they earn at least one hundred thousand dollars, which takes six digits to write! The place value to the left of ten thousands is hundred thousands. There is definitely not room on the page for a picture of this place value! Ten ten thousands makes one hundred thousand.
hundred thousands  ten thousands  thousands  hundreds  tens  ones  

43 467  4  3  2  4  6  7 
803214  8  0  3  2  1  4 
Millions
And if we look one more place to the left, the place value is millions. One million is 1 with six zeros after it: 1 000 000.
A space is left between the millions place and the hundred thousands place. A space is left between the thousands place and the hundreds place.
 2368100
 3150213
 14263942
 5521671
Place values overview
This place value chart may help you to remember the place values.
Notice the groups of three digits. Look at the pattern for the three places which is repeated in each place value group – the pattern is hundreds, tens, ones.
[latex]\begin{array}{ll} \text{ones place }=& \phantom{10} \text{ one} \\ \text{tens place }=& 10 \text{ ones} \\ \text{hundreds place }=& 10 \text{ tens} \\ \text{thousands place }=& 10 \text{ hundreds} \\ \text{ten thousands place }=& 10 \text{ thousands} \\ \text{hundred thousands place }=& 10 \text{ ten thousands} \\ \text{millions place }=& 10 \text{ hundred thousands} \\ \text{ten millions place }=& 10 \text{ millions} \\ \text{hundred millions place }=& 10 \text{ ten millions} \\ \end{array}[/latex]
… and so on.
Our number system is very tidy. When you learn to use the metric measurement system, you will see the metric system is based on ten just like the number system.
Exercise Three
Write the place value name for each bolded digit. Check your work using the answer key at the end of the exercise.
 23206 – the place value for “3” is thousands
 2468 – the place value for “6” is tens
 622 – the place value for “6”
 92002 – the place value for “9”
 92002 – the place value for the first “0”
 14262 – the place value for “6”
 48076 – the place value for “4”
 5555 – the place value for the second “5”
 12245 – the place value for “5”
 92002 – the place value for the second “0”
 12026 – the place value for the first “2”
 6348 – the place value for “6”
Answers to Exercise Three
 thousands
 tens
 hundreds
 ten thousands
 hundreds
 tens
 ten thousands
 hundreds
 ones
 tens
 thousands
 thousands
Exercise Four
Identify the digit for the place value named. Check your work using the answer key at the end of the exercise.
 thousands 416245
 tens 363482
 ten thousands 36482
 hundreds 1456
 hundred thousands 206415
 thousands 63421
 hundreds 74322
 hundred thousands 685413
 thousands 221300
 ten thousands 10000
 ones 16394
 tens 684
Answers to Exercise Four
 416245 – 6
 363482 – 8
 36482 – 3
 1456 – 4
 206415 – 2
 63421 – 3
 74322 – 3
 685413 – 6
 221300 – 1
 10000 – 1
 16394 – 4
 684 – 8
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.
Numerals under 1000
The numerals from 1 to 12 have special words. These are
 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 numerals from 13 to 19 are
 13 thirteen
 14 fourteen
 15 fifteen
 16 sixteen
 17 seventeen
 18 eighteen
 19 nineteen
The word names for the numbers 20 to 90 are
 20 twenty
 30 thirty
 40 forty
 50 fifty
 60 sixty
 70 seventy
 80 eighty
 90 ninety
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.
Number  Tens Ones 

20  twenty 
21  twentyone 
22  twentytwo 
23  twentythree 
24  twentyfour 
25  twentyfive 
26  twentysix 
27  twentyseven 
28  twentyeight 
29  twentynine 
Number  Tens Ones 

30  thirty 
31  thirtyone 
32  thirtytwo 
33  thirtythree 
34  thirtyfour 
35  thirtyfive 
36  thirtysix 
37  thirtyseven 
38  thirtyeight 
39  thirtynine 
Number  Tens Ones 

40  forty 
41  fortyone 
42  fortytwo 
43  fortythree 
44  fortyfour 
45  fortyfive 
46  fortysix 
47  fortyseven 
48  fortyeight 
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).
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.
Example C
[latex]\begin{array}{llll} \textbf{367} \text{ is made of}&\textbf{3} \text{ hundreds}&\textbf{6} \text{ tens}&\textbf{7} \text{ ones}\\ \text{Each part is written:}&\text{three hundreds}&\text{sixty}&\text{seven}\end{array}\\ \text{Put the parts together: }\textbf{three hundred sixtyseven}[/latex]
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
Here is another example. Watch out for the empty space!
Example D
[latex]\begin{array}{llll} \textbf{5054} \text{ is made of}&\textbf{5} \text{ hundreds}&\textbf{0} \text{ tens}&\textbf{4} \text{ ones}\\ \text{Each part is written:}&\text{five hundreds}&&\text{4}\end{array}\\ \text{Put the parts together: }\textbf{five hundred four}[/latex]
Here is another example. Watch out for the empty space!
Example E
Here is another example. Watch out for the empty spaces!
Example F
Remember: empty spaces are not written in words.
Numerals over 1000
Large numerals are read in the place value groups of three that you noticed in the place value chart. You have been practicing reading numerals with three digits or less. Now practice reading the thousands group.
Example G
hundred thousands  ten thousands  thousands  hundreds  tens  ones  

Numeral digits  4  2  3  7  9  6 
Numeral words  four hundred  twenty  three thousand  seven hundred  ninety  six 
Each is written:
 The thousands group is written: four hundred twentythree thousand.
 The hundreds, tens, and ones are written: seven hundred ninety six.
Put the parts together: 423 796 is four hundred twentythree thousand seven hundred ninetysix.
hundred thousands  ten thousands  thousands  hundreds  tens  ones  

26 201 is made of  [empty]  2  6  2  0  1 
Each is written  twentysix thousand  two hundred  [empty]  one  
Put the parts together  twentysix thousand two hundred one 
26 201 is twentysix thousand two hundred one.
hundred thousands  ten thousands  thousands  hundreds  tens  ones  

400 000 is made of  4  0  0  0  0  0 
Each is written  four hundred thousand  
Put the parts together  four hundred thousand 
400 000 is four hundred thousand.
Exercise Five
Write the word names for the numerals. Check your work using the answer key at the end of the exercise.
 491200
hundred thousands ten thousands thousands hundreds tens ones Numeral digits Numeral words  Each is written:
 Thousands:
 Hundreds, tens, ones:
 Put the parts together:
 Each is written:

hundred thousands ten thousands thousands hundreds tens ones 19 631 is made of Each is written Put the parts together 
hundred thousands ten thousands thousands hundreds tens ones 623 009 is made of Each is written Put the parts together  923 471
 53 679
Answers to Exercise Five
 491 200
hundred thousands ten thousands thousands hundreds tens ones Numeral digits 4 9 1 2 0 0 Numeral words four hundred nintey one thousand two hundred  Each is written:
 Thousands: Four hundred ninetyone thousand
 Hundreds, tens, ones: Two hundred
 Put the parts together: Four hundred ninetyone thousand two hundred
 Each is written:

hundred thousands ten thousands thousands hundreds tens ones 19 631 is made of [empty] 1 9 6 3 1 Each is written nineteen thousand six hundred thirty one Put the parts together nineteen thousand six hundred thirtyone 
hundred thousands ten thousands thousands hundreds tens ones 623 009 is made of 6 2 3 0 0 9 Each is written six hundred twentythree thousand [empty] [empty] nine Put the parts together six hundred twentythree thousand nine  nine hundred twentythree thousand four hundred seventyone
 fiftythree thousand six hundred seventynine
Now, just for fun, take a look at these very large numerals. Say ―million for the group to the left of the thousands group.
millions  hundred thousands  ten thousands  thousands  hundreds  tens  ones  

2 643 182 is made of  2  6  4  3  1  8  2 
Each is written  two million  six hundred fortythree thousand  one hundred  eighty  two  
Put the parts together  two million six hundred fortythree thousand one hundred eightytwo 
millions  hundred thousands  ten thousands  thousands  hundreds  tens  ones  

6 510 231 is made of  6  5  1  0  2  3  1 
Each is written  six million  five hundred ten thousand  two hundred  thirty  one  
Put the parts together  six million five hundred ten thousand two hundred thirtyone 
Exercise Six
Write the word names for the numerals. Check your work using the answer key at the end of the exercise.

millions hundred thousands ten thousands thousands hundreds tens ones 2 851 234 is made of Each is written Put the parts together 
millions hundred thousands ten thousands thousands hundreds tens ones 3 186 662 is made of Each is written Put the parts together  3 916 875
 4 873 519
Answers to Exercise Six

millions hundred thousands ten thousands thousands hundreds tens ones 2 851 234 is made of 2 8 5 1 2 3 4 Each is written two million eight hundred fiftyone thousand two hundred thirty four Put the parts together two million eight hundred fiftyone thousand two hundred thirtyfour 
millions hundred thousands ten thousands thousands hundreds tens ones 3 186 662 is made of 3 1 8 6 6 6 2 Each is written three million one hundred eightysix thousand six hundred sixty two Put the parts together three million one hundred eightysix thousand six hundred sixtytwo  three million nine hundred sixteen thousand eight hundred seventyfive
 four million eight hundred seventythree thousand five hundred nineteen
Work on reading these numerals with someone else and then ask your instructor to listen as you read them.
 241962107
 483450
 27800
 2345409
 164231
 260164342
 138000
 410623
 912050
 24900
 227695
 105576
Exercise Seven
Now practice writing numerals from number names. Check your work using the answer key at the end of the exercise.
 Eight hundred twentythree thousand nine hundred fortyone
eight hundred twentythree thousand nine hundred fortyone millions hundred thousands ten thousands thousands hundreds tens ones 8 2 3 9 4 1 823 941  Three million four hundred eightyone thousand five hundred sixtyseven
three million four hundred eightyone thousand five hundred sixty seven millions hundred thousands ten thousands thousands hundreds tens ones 3 4 8 1 5 6 7 3 481 567  Two hundred seventysix thousand five hundred eight
millions hundred thousands ten thousands thousands hundreds tens ones  One million six hundred fiftyeight thousand three hundred twentyfive
millions hundred thousands ten thousands thousands hundreds tens ones  Four million eight hundred sixteen thousand two hundred thirtytwo
millions hundred thousands ten thousands thousands hundreds tens ones  Two hundred seventynine thousand two hundred sixtyone
millions hundred thousands ten thousands thousands hundreds tens ones
Answers to Exercise Seven
 Two hundred seventysix thousand five hundred eight
two hundred seventysix thousand five hundred eight millions hundred thousands ten thousands thousands hundreds tens ones 2 7 6 5 0 8 276 508  One million six hundred fiftyeight thousand three hundred twentyfive
one million six hundred fiftyeight thousand three hundred twentyfive millions hundred thousands ten thousands thousands hundreds tens ones 1 6 5 8 3 2 5 1 658 325  Four million eight hundred sixteen thousand two hundred thirtytwo
four million eight hundred sixteen thousand two hundred thirtytwo millions hundred thousands ten thousands thousands hundreds tens ones 4 8 1 6 2 3 2 4 816 232  Two hundred seventynine thousand two hundred sixtyone
two hundred seventynine thousand two hundred sixtyone millions hundred thousands ten thousands thousands hundreds tens ones 2 7 9 2 6 1 279 261
Exercise Eight
Write the number in each of the word problems. Check your work using the answer key at the end of the exercise.
 The Nile River in Africa is the longest river in the world. It is two thousand five hundred sixtynine kilometers.
 Canada shares a border with the United States that is eight thousand eight hundred ninetythree kilometers.
 The distance around the Earth is forty thousand seventysix kilometers.
 The population of British Columbia in 2009 was four million four hundred fiftyfive thousand two hundred seven.
Answers for Exercise Eight
 2 569 kilometers
 8 893 kilometers
 40 076 kilometers
 4 455 207 people
Topic A: SelfTest
Mark / 17 Aim 14/17
 Write the place value for the underlined digit. (6 marks)
 8765 the place value of 6
 930 the place value of 0
 47932 the place value of 4
 85421 the place value of 5
 279673 the place value of 2
 397 the place value of 3
 Write the numerals for these word names. (5 marks)
 eight hundred fortyseven
 four thousand three hundred eighty
 two hundred seventyfive thousand eightyseven
 sixty thousand four hundred sixteen
 fifteen thousand twenty
 Write the numerals for these word names. (5 marks)
 eight hundred fortyseven
 four thousand three hundred eighty
 two hundred seventyfive thousand eightyseven
 sixty thousand four hundred sixteen
 fifteen thousand twenty
Answers to Topic A SelfTest

 tens
 ones
 ten thousands
 thousands
 hundred thousands
 hundreds

 fiftynine
 nine hundred fortytwo
 seven thousand three hundred seventyeight
 eight thousand two hundred
 four thousand five
 fiftyeight thousand three hundred ten

 847
 4 380
 275 087
 60 416
 15 020