Let’s start with something that you are familiar with:
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