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Understanding Numbers

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Understanding

Numbers

What is a place value

Chart?

Why do you think a place

Value chart would be

Helpful?

Face value is 4

- Each digit in a number has a place value and a face value.
- In the number 4856, the digit 4 is in the thousands place value.
- Meaning the place value is thousands.
- The number you see (4) is the face value.

4856

Place value is thousands

A place value chart helps us to read and understand large numbers.

THOUSANDS

UNITS

ones, tens, hundreds

MILLIONS

- Understand place value helps us say large numbers properly
- When saying large numbers you should:
- A) start with the largest place value grouping
- B) say what you see, then say the grouped place value
- C) continue until all number have been read
4 907 521

- 4 560 392
- 5 500 428
- 5 022 603
- 6 364 210
- 4 321
- 444
- 904 265
- 193 004

- When writing numbers in words you write exactly what you say:
9320 199

- nine million, three hundred twenty thousand, one hundred ninety-nine

- Two hundred sixty four thousand, five hundred three
- Nine million, sixty-two thousand four
- Five million, twenty-two
- Five hundred sixty-three thousand, four hundred thirteen
- Two million, seven thousand, sixteen

Standard and

Expanded Form

- When numbers are presented in numerical digits, it is called the standard form of a number.
4856

Standard Form

- Numbers can also be represented in expanded form.
- This means writing the value of a number using the face value and place value of each digit.
- The number 4856 in expanded form is:
Method a)

4000 + 800 + 50 + 6

Method b)

4 x 1000 + 8 x 100 + 5 x 10 + 6 x 1

- 3982
- 23 508
- 60 000 + 2000 + 900 + 40 + 5
- 800 000 + 50 000 + 300 + 60 + 4
- 3 x 100 000 + 7 x 10 000 + 2 x 1000 +
8 x 100 + 4 x 10 + 5 x 1

- 6 x 100 000 + 2 x 1000 + 8 x 100 +
5 x 10 + 6 x 1

- 30 + 5000 + 300 000 + 200 + 4
- 200 000 + 900 + 4000 + 3 + 10 000
- 6000 + 20 000 + 900 + 400 000 + 5
- 800 000 + 5000 + 3 + 60 + 400
- 3 x 1000 + 7 x 100 000 + 2 x 100 +
8 x 10 000 + 4 x 1 + 5 x 10

- 6 x 10 000 + 2 x 100 000 + 8 x 1000 +
5 x 1 + 6 x 100

Expanded Form

Using Powers of 10

- Numbers can also be written in expanded form using powers of 10
- We will call this expanded form Method C
- Knowing Method A and B makes method C easy

The number 4856 in expanded form is:

Method a)

4000 + 800 + 50 + 6

Method b)

4 x 1000 + 8 x 100 + 5 x 10 + 6 x 1

Method c)

4 x 103 + 8 x 102+ 5 x 101+ 6 x 100

- 32 906
- 53 800
- 40 641
- 7 x 103 + 2 x 102 + 5 x 101 + 3 x 100
- 9 x 105 + 8 x 103 + 7 x 102 + 6 x 101
- 5 x 106 + 2 x 104 + 9 x 103 + 6 x 100