Math Day 2
Powers of Ten
Vocabulary
Place value – the value assigned
to the place that a digit occupies
in a number
2
20
200
2,000
How are these four numbers related?
How are they alike?
How are they different?
In which direction did the digit 2 move when
we multiplied by 10 (instead of 1)?
2,000
200
20
2
││
2 x 10 = 20
2x1=2
2,000
200
20
2
2 x 1,000 = 2,000
2 x 100 = 200
2 x 10 = 20
2x 1 = 2
Can you create a general rule or
relationship for what we’ve just
observed?
Rule: A digit in one place
represents ten times as
much as it represents in
the place to its right.
Why is this rule true?
Ten of the smaller place value make one of the next place value to the left;
therefore a digit in one place represents ten times as much as it represents in the
place to its right.
For example:
10 ones make 1 ten (10 units make 1 rod) so 20 is ten times as big as 2 and the
value of the 2 is ten times as much in 20 as it is in 2.
The same is true for 200, 10 tens make 1 hundred (10 rods make 1 flat) so 200 is
ten times as big as 20 and the value of the 2 in two hundred is ten times as much
as it is in 20.
The same idea is applied to 2,000, 10 hundreds make 1 thousand (10 flats make 1
pack) so 2,000 is ten times as big as 200 and the value of the 2 in two thousand is
ten times as much as it is in 200.)
X
3
30
300
3,000
2
2x3
=6
2 x 30
= 2 x 3 x 10
= 6 x 10
= 60
2 x 300
= 2 x 3 x 100
= 6 x 100
600
2 x 3,000
= 2 x 3 x 1,000
= 6 x 1000
= 6,000
20
20 x 3
= 2 x 10 x 3
= 6 x 10
= 60
20 x 30
= 2 x 10 x 3 x10
= 6 x 100
= 600
20 x 300
= 2 x10 x 3 x 100
= 6 x 1,000
= 6,000
20 x 3,000
= 2 x 10 x 3 x 1,000
= 6 x 10,000
= 60,000
200
200 x 3
= 2 x 100 x 3
= 6 x 100
= 600
200 x 30
= 2 x 100 x 3 x 10
= 6 x 1,000
= 6,000
200 x 300
= 2 x 100 x 3 x 100
= 6 x 10,000
= 60,000
200 x 3,000
= 2 x 100 x 3 x 1,000
= 6 x 100,000
= 600,000
2,000
2,000 x 3 =
2 x 1,000 x 3=
6 x 1,000
6,000
2,000 x 30
= 2 x 1,000 x 3 x 10
= 6 x 10,000
= 60,000
2,000 x 300
= 2 x 1,000 x 3 x 100
= 6 x 100,000
= 600,000
2,000 x 3,000
= 2 x 1,000 x 3 x 1,000
= 6 x 1,000,000
= 6,000,000
•What patterns do you see in each row and column?
•What general rule(s) for multiplying numbers with zeros can you create?