B. Number · Number Sense: Numbers to 100 000, Fractions, Decimals and Percents

Place Value: Building and Breaking Apart Numbers to 100 000

B1.1About 35 minutes

Learning goals

I can tell the value of each digit in a number up to 100 000.
I can write a number in expanded form.
I can break apart (decompose) a number in more than one way.
I can build (compose) a number from parts, even when I have to regroup.

Words to know

place value
The value a digit has because of the place it is in. In 63 482, the 3 is worth 3000.

expanded form
A number written as the sum of its place values: 63 482 = 60 000 + 3000 + 400 + 80 + 2.

standard form
A number written the usual way with digits, like 63 482.

compose
Put parts together to build a number.

decompose
Break a number into parts.

regroup
Trade 10 of one place for 1 of the next place to the left, or 1 for 10 going the other way.

Remember from Grade 4

In Grade 4 you learned that each place is worth 10 times the place to its right: 10 ones make a ten, 10 tens make a hundred, and 10 hundreds make a thousand. You wrote numbers in expanded form, like 3425 = 3000 + 400 + 20 + 5. Now the same rules work for numbers to 100 000.

Let's start with a puzzle

A hockey arena sold 23 145 tickets in one month. The manager has bundles of 10 000 tickets, 1000 tickets, 100 tickets, 10 tickets and single tickets. How could she show 23 145?

2 bundles of 10 000, 3 bundles of 1000, 1 bundle of 100, 4 bundles of 10 and 5 single tickets. That's place value!

The manager's ticket bundles for 23 145: 2 bundles of 10 000, 3 of 1000, 1 of 100, 4 of 10 and 5 single tickets. Each kind of bundle matches one place.

The ×10 pattern keeps going

10 ones = 1 ten (10)
10 tens = 1 hundred (100)
10 hundreds = 1 thousand (1000)
10 thousands = 1 ten thousand (10 000)
10 ten thousands = 1 hundred thousand (100 000)

Ten bars of 1000 together make one bar of 10 000.

Digit in 63 482	Place	Value
6	ten thousands	60 000
3	thousands	3000
4	hundreds	400
8	tens	80
2	ones	2

Each digit in 63 482 and what it is worth.

Expanded form

Add up the values of all the digits:

63 482 = 60 000 + 3000 + 400 + 80 + 2

If a digit is 0, you can leave it out: 50 704 = 50 000 + 700 + 4.

Many ways to break apart a number

Expanded form is only one way. Here are other ways to decompose 63 482:

63 thousands + 4 hundreds + 8 tens + 2 ones
634 hundreds + 82 ones
50 000 + 13 000 + 482

All of these are the same amount. Thinking in different ways makes mental math easier.

Worked example

Example 1: Expanded form with a zero

Write 58 093 in expanded form.

5 ten thousands = 50 000. 8 thousands = 8000.
0 hundreds: nothing to write.
9 tens = 90. 3 ones = 3.

58 093 = 50 000 + 8000 + 90 + 3

Worked example

Example 2: Same digit, different value

What is each 7 worth in 77 470?

The first 7 is in the ten thousands place: 70 000.
The second 7 is in the thousands place: 7000.
The third 7 is in the tens place: 70.

70 000, 7000 and 70. The place changes the value. The first 7 is worth 10 times the second 7.

Worked example

Example 3: Compose with regrouping

What number is 4 ten thousands + 12 thousands + 5 hundreds + 3 ones?

4 ten thousands = 40 000.
12 thousands = 12 000. That's more than 9 thousands, so we will need to regroup.
40 000 + 12 000 = 52 000.
Add the rest: 52 000 + 500 + 3 = 52 503.

52 503

Worked example

Example 4: Thinking in hundreds

A bank machine gives out only $100 bills. How many bills make $36 500?

36 500 = 36 thousands + 5 hundreds.
Each thousand is 10 hundreds, so 36 thousands = 360 hundreds.
360 hundreds + 5 hundreds = 365 hundreds.

365 bills of $100.

Cover-up trick

To find how many hundreds are in a number, cover the tens and ones digits with your fingers. What's left is the number of hundreds! In 36 500, cover "00" and you see 365. The same trick works for thousands: cover the last three digits of 36 500 and you see 36 thousands.

Place value riddle

I am a 5-digit number. All of my digits are the same, and they add up to 35. What number am I?

77 777! Five 7s make 35.

Hands-on activity

Paper money bank

You need: paper, a pencil, and safety scissors or a grown-up to help cut.

Cut paper into small slips. Make 10 slips each of: $10 000, $1000, $100, $10 and $1. (Write the amount on each slip.)
Your grown-up says a number, like 34 251. Build it with the fewest slips. Then say it in expanded form.
Build 27 000 in two different ways. (Hint: 10 slips of $100 make the same amount as one $1000 slip.)
Trade: swap 10 of your $1000 slips for one $10 000 slip. Is the amount the same?
Make up a number for your grown-up to build.

Check for step 3: one way is 2 slips of $10 000 + 7 slips of $1000. Another way is 2 slips of $10 000 + 6 slips of $1000 + 10 slips of $100.

Your turn

Write 47 236 in expanded form.

What is the value of the 9 in 29 615?

Write in standard form: 80 000 + 4000 + 50 + 1

How many thousands are in 25 000?

How many hundreds are in 25 000?

10 thousands = ?

What number is 6 ten thousands + 2 thousands + 7 tens?

More practice: warm-up

30 000 + 5000 + 400 + 20 + 1 = ?

Which digit is in the ten thousands place in 71 806?

What is the value of the 8 in 71 806?

10 × 1000 = ?

Write 90 300 in expanded form.

More practice: on your own

What number is 3 ten thousands + 15 thousands + 2 hundreds?

How many hundreds are in 52 400?

Decompose 64 000 in two different ways.

Mia says the 4 in 14 532 is worth 4. Is she right?

A bank machine gives only $100 bills. How many bills for $12 000?

Challenge

I have 2 ten thousands, 23 thousands, 14 hundreds and 6 ones. What is my number?

In 55 000, how many times greater is the value of the first 5 than the value of the second 5?

Paper clips come in boxes of 100. There are 10 boxes in a carton. How many cartons hold 100 000 paper clips?

Check your understanding

Quiz

Which is 40 572 in expanded form?

What is the value of the 6 in 86 213?

10 thousands is the same as...

Which number is 3 ten thousands + 4 hundreds + 2 ones?

How many hundreds are in 15 000?

2 ten thousands + 11 thousands = ?

For parents and teachers

Big idea: This lesson continues B1.1: composing and decomposing numbers to 100 000. Knowing that 63 482 is also 634 hundreds + 82, or 63 thousands + 482, is a powerful tool for mental math and for the larger calculations in the Operations unit.

Common difficulties:

Confusing the digit with its value. "The 4 in 14 532" is worth 4000, not 4. Ask "What is it worth?" not just "What digit is it?"
Regrouping when composing. 12 thousands is more than 9 thousands, so it makes 1 ten thousand and 2 thousands. Play money makes this concrete.
Thinking expanded form is the only way. Praise any correct decomposition.

How to help: Use money: "How many $100 bills would a $27 500 car cost?" (275.) Ask your child to say numbers in two ways: "forty-two thousand" is also "42 thousands" or "420 hundreds". If you cut paper slips for the activity, supervise scissor use.