The distance from New York City to
San Francisco is 2.905 x 103 miles. How
does multiplying the number 2.905 by
103 change its value?
New York City
San Francisco
In this lesson you will learn how
multiplying by a power of ten
increases a digit’s value by using
patterns in place value.
Let’s Review
You can find the relationship between
place values by multiplying or dividing by
ten.
10 x 10 = 100
10 x 10 x
.
.
Tenths
Ones
Tens
329
9
Thousandths
Thousandths
Hundredths
Ones
Hundreds
Hundred
Thousands
Ten
Thousands
941
900
Thousands
Thousands
Millions
Ten Millions
Hundred
Millions
Millions
Let’s Review
A power of ten is a special notation, called
scientific notation, in which the base
number is always ten.
1
10 = 10 x 1 = 10
2
1 = 10 x 10 = 100
3
0
10 = 10 x 10 x 10 = 1,000
4
10 = 10 x 10 x 10 x 10 = 10,000
5
10 = 10 x 10 x 10 x 10 x 10 = 100,000
Core Lesson
When you multiply a number by a power of
ten, the value of each digit increases ten
times for each power.
0
4 .
Thousandths
.
Hundredths
0
Thousandths
Ones
0
Tens
0
Ones
Hundreds
0
Thousands
Hundred
Thousands
Ten
Thousands
Thousands
Millions
Ten Millions
Hundred
Millions
Millions
Tenths
4 x 10
2
3
4
5
1
Core Lesson
When you multiply a number by a power of
ten, the value of each digit increases ten
times for each power.
1
4 x 10 = 4 x 10 = 40
2
4 x 10 = 4 x 100 = 400
3
4 x 10 = 4 x 1,000 = 4,000
4
4 x 10 = 4 x 10,000
5
= 40,000
4 x 10 = 4 x 100,000 = 400,000
Core Lesson
When you multiply a number by a power of
ten, the value of each digit increases ten
times for each power.
0.692 x 10
Tenths
Hundredths
Thousandths
0
Thousandths
0 . 6
9
2
Ones
Tens
Ones
Hundreds
Thousands
Hundred
Thousands
Ten
Thousands
Thousands
Millions
Ten Millions
Hundred
Millions
Millions
4
15
3
2
.
Core Lesson
When you multiply a number by a power of
ten, the value of each digit increases ten
times for each power.
1
0.692 x 10 = 0.692 x 10 = 6.92
0.692 x 10 2 = 0.692 x 100 = 69.2
0.692 x 10 3 = 0.692 x 1,000
4
0.692 x 10 = 0.692 x 10,000
0.692 x 10 5 = 0.692 x 100,000
= 692.
= 6,920.
= 69,200.
A Common Misunderstanding
Thinking that you simply add a zero to the
end of a number for each power you
multiply by.
3
6 x 10 = 6 x
10
3
x
10
x 10 = 6,6
06
06
0
.157 x 10 = .157 x
x
x 10 = .157
15.7
1.57
157
10 10
3
.157 x 10 ≠ .157000
Core Lesson
The distance from New York City to San
Francisco is 2.905 x 103 miles. How does
multiplying the number 2.905 by 103
change its value?
2.905 x 103 = 2.905 x 1,000
= 2,905 miles
In this lesson you have learned
how multiplying by a power of
ten increases a digit’s value by
using patterns in place value.