# Multiply & Divide Powers of 10 – Mini-Tutorial

1

-------  =  0.01

100

As you already know, when any number is divided by 100, it moves the decimal two places to the left.

You may not be familiar with this, but if not, it is time to get used to it.

1 x 103  =  1,000

1 x 10-2  =  0.01

This means that a negative power of 10 (-2 in our example above)  moves the decimal to the left by the value of the negative power.  Let’s look at another example:

15.37

--------  =  0.01537                   and               15.37  x  10-3  =  0.01537

1,000

15.37

----------  =  0.001537              and                 15.37 x 10-4  =  0.001537

10,000

What happens when we divide a number by a power of 10?   Let’s see:

135                                                                  135

------  =  135  x  10-2  =  1.35             and       ------  =  1.35

102                                                                  100

For this reason, what happens when a power of 10 is moved from the bottom to the top of a fraction?   That is right, we change the sign of the power of 10.  In the last example, the power of 10 was 2   (102).   We changed the sign from 2 to –2 (102 changed to 10-2).

So dividing by powers of 10 means that we change the sign of the power of 10.

Work out these examples to see if you get it now  (answers are down below):

1089

a.    --------  =  ?

103

386

b.     ------  =  ?

10-2

0.0587

c.    ---------  =  ?

107

0.0587

d.    ---------  =  ?

10-7

Ans:      a.  1.089        b.  38,600     c.  0.00000000587     d.  587,000

Now let’s see what happens when we use that big, huge number.  See if you can get your powers of ten right on this problem (answers are below):

48 g O          1 mole O          6.022 x  1023 atoms O

a.       ----------  x  ------------  x  --------------------------   =  ?  atoms O   (use scientific notation)

1                 16 g O                  1 mole O

1.54 x 1018 atoms K             1 mole K

b.         ---------------------- x ------------------- = ? moles K  (use scientific notation)

1                      6.022 x 1023 K

Ans:    a.  18 x 1023 atoms O  =  1.8 x 1024 atoms O

b.  0.256 x  10-5  moles K  =   2.56 x 10-4 moles K