# Whole numbers: Place values, standard and expanded forms

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### Review

• Whole numbers are integers, with no fraction or decimal and no negatives. eg. 3, 9, 62.
• A digit is any number 0-9.
• The largest digit that can be used in any place is 9 and the smallest is 0.

### What are place values?

“Ones, tens, and hundreds,
Thousands, ten thousands, and Hundred thousands,
Millions, ten millions, hundred millions,
Billions, ten billions, hundred billions,
and TRILLIONS!
These are the place values!”

• Place is where a digit sits in a number.
• Value is how much this digit is worth!

### What are the standard, expanded and word forms?

• Standard form = the number itself.
• Expanded form = the number expanded out into the sum of the value of its digits (so 234 = 200 + 30 + 4)
• Word form = the number spelled out in words, the way we say it.

### Examples? Yes, of course!

1. 23 (tens and ones)
23 = 20 + 3
So 20 is in the ten’s place, and 3 is in the one’s place.
Word form: Twenty three.
Standard form: 23
Expanded form: 20 + 3

2. 346 (hundreds, tens and ones)
346 = 300 + 40 + 6
300 is in the hundred’s place, 40 is in the ten’s place, and 6 is in the one’s place.
Word form: Three hundred forty six.
Standard form: 346
Expanded form: 300 + 40 + 6

3. 2,479 (thousands, hundreds, tens and ones)
2,479 = 2,000 + 400 + 70 + 9
2,000 is in the thousand’s place, 400 is in the hundred’s place, 70 is in the ten’s place and ten’s place, and 9 is in the one’s place.
Word form: Two thousand, four hundred and seventy nine.
Standard form: 2,479
Expanded form: 2,000 + 400 + 70 + 9

4. 91,234 (ten thousands, thousands, hundreds, tens and ones)
91,234 = 90,000 + 1,000 + 200 + 30 + 4
90,000 is in the ten thousand’s place, 1,000 is in the thousand’s place, 200 is in the hundred’s place, 30 is in the ten’s place, and 4 is in the one’s place.
Word form: Ninety one thousand, two hundred and thirty four.
Standard form: 91,234
Expanded form: 90,000 + 1,000 + 200 + 30 + 4

5. 899,458 (hundred thousands, ten thousands, thousands, hundreds, tens and ones)
899,458 = 800,000 + 90,000 + 9,000 + 400 + 50 + 8
800,000 is in the hundred thousand’s place, 90,000 is in the ten thousand’s place, 9,000 is in the thousand’s place, 400 is in the hundred’s place, 50 is in the ten’s place, and 8 is in the one’s place.
Word form: Eight hundred ninety nine thousand, four hundred and fifty eight.
Standard form:  899,458
Expanded form: 800,000 + 90,000 + 9,000 + 400 + 50 + 8

6. 1,921,234 (millions, hundred thousands, ten thousands, thousands, hundreds, tens and ones)
1,921,234 = 1,000,000 + 900,000 + 20,000 + 1,000 + 200 + 30 + 4
1,000,000 is in the million’s place, 900,000 is in the hundred thousand’s place, 20,000 is in the ten thousand’s place, 1,000 is in the thousand’s place, 200 is in the hundred’s place, 30 is in the ten’s place, and 4 is in the one’s place.
Word form: One million, nine hundred twenty one thousand, two hundred and thirty four.
Standard form:  1,921,234
Expanded form: 1,000,000 + 900,000 + 20,000 + 1,000 + 200 + 30 + 4

7. 41,921,234 (ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens and ones)
41,921,234 = 40,000,000 + 1,000,000 + 900,000 + 20,000 + 1,000 + 200 + 30 + 4
40 million is in the ten millions place, 1,000,000 is in the million’s place, 900,000 is in the hundred thousand’s place, 20,000 is in the ten thousand’s place, 1,000 is in the thousand’s place, 200 is in the hundred’s place, 30 is in the ten’s place, and 4 is in the one’s place.
Word form: Forty one million, nine hundred twenty one thousand, two hundred and thirty four.
Standard form:  41,921,234
Expanded form: 40,000,000 + 1,000,000 + 900,000 + 20,000 + 1,000 + 200 + 30 + 4

8. 541,921,234 (hundred millions, ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens and ones)
541,921,234 = 500,000,000 + 40,000,000 + 1,000,000 + 900,000 + 20,000 + 1,000 + 200 + 30 + 4
500 million is in the hundred millions place, 40 million is in the ten millions place, 1,000,000 is in the million’s place, 900,000 is in the hundred thousand’s place, 20,000 is in the ten thousand’s place, 1,000 is in the thousand’s place, 200 is in the hundred’s place, 30 is in the ten’s place, and 4 is in the one’s place.
Word form: Five hundred forty one million, nine hundred twenty one thousand, two hundred and thirty four.
Standard form:  541,921,234
Expanded form: 500,000,000 + 40,000,000 + 1,000,000 + 900,000 + 20,000 + 1,000 + 200 + 30 + 4

9. 2,541,921,234 (billion, hundred millions, ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens and ones)
2,541,921,234 = 2,000,000,000 + 500,000,000 + 40,000,000 + 1,000,000 + 900,000 + 20,000 + 1,000 + 200 + 30 + 4
2 billion is in the billions place, 500 million is in the hundred millions place, 40 million is in the ten millions place, 1,000,000 is in the million’s place, 900,000 is in the hundred thousand’s place, 20,000 is in the ten thousand’s place, 1,000 is in the thousand’s place, 200 is in the hundred’s place, 30 is in the ten’s place, and 4 is in the one’s place.
Word form: Two billion, five hundred forty one million, nine hundred twenty one thousand, two hundred and thirty four.
Standard form:  2,541,921,234
Expanded form: 2,000,000,000 + 500,000,000 + 40,000,000 + 1,000,000 + 900,000 + 20,000 + 1,000 + 200 + 30 + 4

Tips and tricks to remember your place values:

A thousand has 3 zeros.

A million has 6 zeros.

A billion has 9 zeros

A trillion has 12 zeros

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