In the table at right, write each power of $10$ as a decimal and as a fraction.

• 1. Describe how the decimals and fractions change as you progress down the table.

     Hint (a):

     $10^{0} = 1$
     $10^{−2} = 0.01$

     Do you notice any patterns? Try to fill in the rest of the table on your own.

     More Help (a):

     Notice that the decimal point moves to the left one spot as the value of the exponent decreases, while the denominator in the fraction form increases by a multiple of $10$.

  2. How would you tell someone how to write $10^{−12}$ as a fraction? You do not have to write the actual fraction.

     Hint (b):

     From the table, you see that the magnitude of the exponent corresponds to the number of zeros in the denominator of the fraction form of the number.

     Answer (b):

     Therefore the fraction form of this number would have $1$ over a denominator of $1$ with $12$ zeros following.