Multiply & Divide Powers of 10 Ė Mini-Tutorial

 

Letís 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.Letís look at another example:

 

††††††††††† 15.37

†††††††††† -------- =0.01537†††††††††††††††††† and†††††††††††††† 15.37x10-3=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?†† Letís see:

 

††††††††††† 135††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† 135

††††††††† ------=135x10-2=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 Ė2 (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 letís 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 x1023 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