Math Day 2

Powers of Ten

Vocabulary

Place value – the value assigned to the place that a digit occupies in a number

2 20200

2,000How 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

2 x 1 = 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 2 x 3= 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 1,0006,000

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?