Remember This?
How Big? How Small?

Print this worksheet and complete the activities.

1) Do you remember what happens when you multiply a number by 10? By 100? By 1000?

Try these problems and test your skill:

25 x 10 =
34 x 100 =
564 x 1000 =

Too Easy?

3.4 x 10 =
4.56 x 100 =
3.56 x 1000 =
4.5673 x 100 =
0.0075634 x 1000 =

Describe the pattern that you see developing in these calculations.

2) Do you remember what happens when you divide a number by 10? By 100? By 1000?

Try these problems and test your skill:

45 ÷ 10 =
356 ÷ 100 =
456 ÷ 1000 =
35.6 ÷ 10 =
64.56 ÷ 100 =
465.345 ÷ 1000 =
0.765 ÷ 10 =
0.345 ÷ 100 =
0.00856 ÷ 1000 =

Describe the pattern that is illustrated by these calculations.

3) Powers of ten can also be described by using exponential notation, and multiplication and division problems can be written using this notation.

101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10,000
105 = 10 x 10 x 10 x 10 x 10 = 100,000

Get the picture?

So our multiplication problems could have been written as:

25 x 10 =
34 x 102 =
564 x 103 =
3.4 x 10 =
4.56 x 102 =
3.56 x 103 =

And so on.

Dividing by powers of ten is equivalent to multiplying by negative powers to ten. For example:

45 ÷ 10 = 45 x (1 ÷ 10) = 45 x 10-1
64.56 ÷ 100 = 64.56 x 10-2
1 ÷ 10 = 10-1
1 ÷ 100 = 1 ÷ 102=10-2
1 ÷ 1000 = 1 ÷ 103 = 10-3
1 ÷ 10,000 = 1 ÷ 104 = 10-4

We can use these ideas to write numbers in scientific notation.

Numbers that are written in scientific notation look like this:

9,000,000 = 9.0 x 106

or

0.000675 = 6.75 x 10-4

or in general terms

Y= a x 10n

4) In order to write numbers in scientific notation, you need to do the following:

 a) Move the decimal point to a position immediately following the first nonzero digit in Y.

 b) Count the number of places the decimal point has been moved. This is the exponent, n, to which 10 is raised.
  • If the decimal point is moved to the left, n is positive.
  • If the decimal point is moved to the right, n is negative.
  • If the decimal point already follows the first nonzero digit, n is zero.
5) In order to write numbers in scientific notation in standard form, you need to do the following:

When the exponent in 10n is:
  • Positive, the decimal point is moved to the right n places.
  • Negative, the decimal point is moved to the left n places.
  • Zero, the decimal point is not moved.
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