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 | |
|---|---|---|---|---|---|---|
| 432 467 | 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 | twenty-one |
| 22 | twenty-two |
| 23 | twenty-three |
| 24 | twenty-four |
| 25 | twenty-five |
| 26 | twenty-six |
| 27 | twenty-seven |
| 28 | twenty-eight |
| 29 | twenty-nine |
| Number | Tens Ones |
|---|---|
| 30 | thirty |
| 31 | thirty-one |
| 32 | thirty-two |
| 33 | thirty-three |
| 34 | thirty-four |
| 35 | thirty-five |
| 36 | thirty-six |
| 37 | thirty-seven |
| 38 | thirty-eight |
| 39 | thirty-nine |
| Number | Tens Ones |
|---|---|
| 40 | forty |
| 41 | forty-one |
| 42 | forty-two |
| 43 | forty-three |
| 44 | forty-four |
| 45 | forty-five |
| 46 | forty-six |
| 47 | forty-seven |
| 48 | forty-eight |
| 49 | forty-nine |
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 ninety-nine (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 sixty-seven}[/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{504} \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 twenty-three thousand.
- The hundreds, tens, and ones are written: seven hundred ninety six.
Put the parts together: 423 796 is four hundred twenty-three thousand seven hundred ninety-six.
| hundred thousands | ten thousands | thousands | hundreds | tens | ones | |
|---|---|---|---|---|---|---|
| 26 201 is made of | [empty] | 2 | 6 | 2 | 0 | 1 |
| Each is written | twenty-six thousand | two hundred | [empty] | one | ||
| Put the parts together | twenty-six thousand two hundred one |
26 201 is twenty-six 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 ninety-one thousand
- Hundreds, tens, ones: Two hundred
- Put the parts together: Four hundred ninety-one 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 thirty-one -
hundred thousands ten thousands thousands hundreds tens ones 623 009 is made of 6 2 3 0 0 9 Each is written six hundred twenty-three thousand [empty] [empty] nine Put the parts together six hundred twenty-three thousand nine - nine hundred twenty-three thousand four hundred seventy-one
- fifty-three thousand six hundred seventy-nine
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 forty-three thousand | one hundred | eighty | two | ||
| Put the parts together | two million six hundred forty-three thousand one hundred eighty-two |
| 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 thirty-one |
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 fifty-one thousand two hundred thirty four Put the parts together two million eight hundred fifty-one thousand two hundred thirty-four -
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 eighty-six thousand six hundred sixty two Put the parts together three million one hundred eighty-six thousand six hundred sixty-two - three million nine hundred sixteen thousand eight hundred seventy-five
- four million eight hundred seventy-three 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 twenty-three thousand nine hundred forty-one
eight hundred twenty-three thousand nine hundred forty-one millions hundred thousands ten thousands thousands hundreds tens ones 8 2 3 9 4 1 823 941 - Three million four hundred eighty-one thousand five hundred sixty-seven
three million four hundred eighty-one 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 seventy-six thousand five hundred eight
millions hundred thousands ten thousands thousands hundreds tens ones - One million six hundred fifty-eight thousand three hundred twenty-five
millions hundred thousands ten thousands thousands hundreds tens ones - Four million eight hundred sixteen thousand two hundred thirty-two
millions hundred thousands ten thousands thousands hundreds tens ones - Two hundred seventy-nine thousand two hundred sixty-one
millions hundred thousands ten thousands thousands hundreds tens ones
Answers to Exercise Seven
- Two hundred seventy-six thousand five hundred eight
two hundred seventy-six 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 fifty-eight thousand three hundred twenty-five
one million six hundred fifty-eight thousand three hundred twenty-five 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 thirty-two
four million eight hundred sixteen thousand two hundred thirty-two millions hundred thousands ten thousands thousands hundreds tens ones 4 8 1 6 2 3 2 4 816 232 - Two hundred seventy-nine thousand two hundred sixty-one
two hundred seventy-nine thousand two hundred sixty-one 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 sixty-nine kilometers.
- Canada shares a border with the United States that is eight thousand eight hundred ninety-three kilometers.
- The distance around the Earth is forty thousand seventy-six kilometers.
- The population of British Columbia in 2009 was four million four hundred fifty-five thousand two hundred seven.
Answers for Exercise Eight
- 2 569 kilometers
- 8 893 kilometers
- 40 076 kilometers
- 4 455 207 people
Topic A: Self-Test
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 word names for these numerals. (6 marks)
- 59
- 942
- 7378
- 8200
- 4005
- 58310
- Write the numerals for these word names. (5 marks)
- eight hundred forty-seven
- four thousand three hundred eighty
- two hundred seventy-five thousand eighty-seven
- sixty thousand four hundred sixteen
- fifteen thousand twenty
Answers to Topic A Self-Test
-
- tens
- ones
- ten thousands
- thousands
- hundred thousands
- hundreds
-
- fifty-nine
- nine hundred forty-two
- seven thousand three hundred seventy-eight
- eight thousand two hundred
- four thousand five
- fifty-eight thousand three hundred ten
-
- 847
- 4 380
- 275 087
- 60 416
- 15 020