Watch the following video to review expanded form.
Think about:
In expanded form we multiply each place value by ones, tens, hundreds, thousands, etc... How would we do the same operation if we only used 10 in our operation?
Exponent Review
Practice:
Your turn now, try figuring out the expanded form and standard form in your notebook
| Exponent Form |
Expanded Form |
Standard Form |
| 38 |
3x3x3x3x3x3x3x3 |
6,561 |
| 57 |
5x5x5x5x5x5x5 |
78,125 |
| 48 |
4x4x4x4x4x4x4x4 |
65,536
|
| 53 |
5x5x5 |
125 |
| 47 |
4x4x4x4x4x4x4 |
16,384 |
| 76 |
7x7x7x7x7x7 |
117,649 | Think About:
Now try filling out the following chart using powers of ten. What do you notice? How can we use this using the knowledge we have with expanded form?
| Exponent Form |
Expanded Form |
Standard Form |
| 10-2 |
1/10 x 1/10 |
1/100 = 0.01 |
| 10-1 |
1/10 |
1/10 = 0.1 |
| 100 |
1 |
1 |
| 101 |
10 x 1 |
10 |
| 102 |
10 x 10 |
100 |
| 103 |
10 x 10 x 10 |
1,000 |
| 104 |
10 x 10 x 10 x 10 |
10,000 |
| 105 |
10 x 10 x 10 x 10 x 10 |
100,000 |
| 106 |
10 x 10 x 10 x 10 x 10 x 10 |
1,000,000 |
| 107 |
10 x 10 x 10 x 10 x 10 x 10 x 10 |
10,000,000 |
| 108 |
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 |
100,000,000 |
| 109 |
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 |
1,000,000,000 |
| 1010 |
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 |
10,000,000,000 |
Now try using all the new forms to show the same number:
| Standard Form |
Expanded Form with base 10 |
Expanded Form with powers of 10 |
| 501.05 |
5x 100 + 1 x 1 + 5 x 0.01 |
5 x 102 + 1 x 100 + 5 x 10-2 |
| 55,360,085 |
|
|
| 990, 661 |
|
|
| 18, 701 |
|
|
| 330.51 |
|
|
| 88,660.001 |
8 x 10000 + 8 x 1000 + 6 x 100 + 6 x 10 + 1 x 0.001 |
8 x 10 4 + 8 x 103 + 6 x 102 + 6 x 101 + 1 x 10-3 |
| 56.1005 |
(5x10)+(6x1)+(1x0.01)+(5x0.0001) |
5x101 + 6x100 + 1x10-1 +5x10-4 |
| 654,500.008 |
|
|
| 11,585.043 |
|
| |
|
