Evaluate
10 x 1 = 10
Power
of 10
101
10 x 10 = 100
102
10 x 10 x 10 = 1,000
103
10 x 10 x 10 x 10 = 10,000
104
10 x 10 x 10 x 10 x 10 = 100,000
105
10 x 10 x 10 x 10 x 10 x 10 = 1,000,000
106
10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000
107
Describe any patterns you see in the “Evaluate” column.
I notice that when you multiply 10 x 10, the 1 in the tens place moves one place to the left and
has a value of one hundred now This same idea can be applied to the rest of the equations. I
also notice that each time I multiply by another 10, there is one more zero in the product. This
makes sense based on what I’ve learned about place value. I realize that each time I move down
a row, I’m multiplying the previous product by 10 (since I have just one more ten to multiply by
each time I move down in the chart). Multiplying by ten means each digit will move one place
value to the left since ten in one place value makes one in the place value to its left.
Describe what you notice about the exponents in the “Power of 10” column.
Students should reason that the exponent above the 10 tells how many tens they are multiplying
(or how many times ten is being used as a factor). They should also notice that the exponent
above the ten is the same as the number of zeros in the product. For example, in 105 the
exponent is 5 and in the product there are 5 zeros (100,000). . Multiplying by ten one time shifts
each digit to the left one place. So if they multiply by ten more than one time, each digit with
shift that many places to the left.
Evaluate
25 x 101 = 25 x 10 = 250
25 x 102 = 25 x 10 x 10 = 25 x 100 = 2,500
25 x 103 = 25 x 10 x 10 x 10 = 25 x 1,000 = 25,000
25 x 104 = 25 x 10 x 10 x 10 x 10 = 25 x 10,000 = 250,000
25 x 105 = 25 x 10 x 10 x 10 x 10 x 10 = 25 x 100,000 = 2,500,000
Identify and describe any patterns you see.
I noticed that every time I multiplied by 10 there was one more zero on the end of
the product. That makes sense because each digit’s value became 10 times larger.
To make a digit 10 times larger, I have to move it one place value to the left. When
I multiplied 25 by 10, the 20 became 200. The 5 became 50 or the 25 became 250.
So I had to place a zero at the end to have the 2 represent 2 one-hundreds (instead
of 2 tens) and the 5 represents 5 tens (instead of 5 ones).
Expression
39.45 x 101
Solution (Show your work)
39.45 x 101 = 39.45 x 10 =
394.5
9.78 x 103
9.78 x 103 = 9.78 x 1,000 =
9,780
Place Value Explanation
The decimal moved one place to the
right. The place value of 39.45
increased by one place since the
exponent is 1 and I multiplied by 10.
The 30 now has a value of 300, the 9
now has a value of 90, the 0.4 now has
a value of 4 and the 0.05 now has a
value of 0.5.
The decimal moved three places to the
right. The place value of 9.78
increased by three places since the
exponent is 3 and I multiplied by
1,000. The 9 now has a value of 9,000,
the 0.7 now has a value of 700, and the
0.08 now has a value of 80. I had to
place a zero at the end of the number
since the decimal moved three places.
100.4 x 104
100.4 x 104 = 100.4 x
10,000 = 1,004,000
5.567x 102
5.567x 102 = 5.567 x 100 =
556.7
Create your
own.
Answers will vary
The decimal moved four places to the
right. The place value of 100.4
increased by four places since the
exponent is 4 and I multiplied by
10,000. The 100 now has a value of
1,000,000, the 0.4 now has a value of
4,000, and I had to place three zeros at
the end of the number since the
decimal moved four places.
The decimal moved two places to the
right. The place value of 5.567
increased by two places since the
exponent is 2 and I multiplied by 100.
The 5 now has a value 500, the 0.5
now has a value of 50, the 0.06 now
has a value of 6 and the 0.007 now has
a value of 0.7.
Answers will vary
Answers will
vary
When I multiply a decimal by a power of 10, the decimal moves to the
right. To determine the number of places the decimals moves to the right, I just
have to look at the exponent. The fact that the decimal moves to the right makes
sense since I know multiplying by a power of 10 increases the value of the number
(the value of each digit increases ‘n’ places, when ‘n’ is the exponent).