Notes

Representing Numbers Using Powers of 10
Name: _______________________________ Date: _________________

1

Learning Goal
I can use powers of 10 to describe any whole number.
Lesson Summary
• You can describe the columns we use in place value using powers of 10.
Millions Hundred
thousands
Ten
thousands

Thousands Hundreds Tens Ones

10 6 10 5 10 4 10 3 10 2 10 1
Powers of 10 make sense because each column in the place-value chart is
10 times as much as the column to its right.
For example, a 1 in the hundreds column represents 100, which is 10 × 10,
or 10 2 .
A 1 in the thousands column represents 1000 — 10 times as much as 100 —
because 1000 = 10 × 10 × 10, or 10 3 .
• You have learned to write numbers that are in standard form in expanded form
in several ways. For example, the number 123 145 can be written like this:
1 hundred thousand + 2 ten thousands + 3 thousands + 1 hundred + 4 tens +
5 ones or as
100 000 + 20 000 + 3000 + 100 + 40 + 5.
• You have also learned to write numbers in expanded form using powers of 10:
The number 123 145 can be written like this:
1 × 10 5 + 2 × 10 4 + 3 × 10 3 + 1 × 10 2 + 4 × 10 1 + 5.
The number that is multiplied by each power of 10 is a digit in the original
number.
• If one of the digits of a number is 0, include 0 multiplied by that power of 10, or
omit that power of 10. For example, you can write 300 204 in one of these ways:
3 × 10 5 + 2 × 10 2 + 4 or
3 × 10 5 + 0 × 10 4 + 0 × 10 3 + 2 × 10 2 + 0 × 10 1 + 4.

Key Terms
expanded form: a way to represent a number to show the value of each digit;
for example, 541 607 is 500 000 + 40 000 + 1000 + 600 + 7 OR 5 hundred
thousands + 4 ten thousands + 1 thousand + 6 hundreds + 7 ones OR 5 × 10 5 +
4 × 10 4 + 1 × 10 3 + 6 × 10 2 + 7

Representing Numbers Using Powers of 10 (continued)
Name: ________________________ Date: ___________

2

standard form: the usual form of a number, that is, the numeral, for example, 3456
power of 10: a number that is written as 10 n , for example, 10 1 , 10 2 , 10 3 , etc.