Yes, Understand 3 + 375/1000. Thanks\
But when problem says "Show that each decimal can be written as a quotient of two integers. Ex. 3.375 ; Ex. .18 ; etc. Dont' know how to do that.
Thanks for all the help you can give to get me on my way.
A rational number can be expressed in many ways, ONE of which is in decimal form.
The normal definition of a rational number is that it is one integer divided by another integer (other than zero).
Example \(\displaystyle 0.5 = \dfrac{1}{2} = \dfrac{2}{4} = \dfrac{3}{6} = \dfrac{4}{8} = \dfrac{5}{10}....\)
These are all different ways to express the same rational number.
So every number represented in decimal form can be expressed in terms of a fraction, the denominator of which is a power of 10, and the numerator of which is your original number without a decimal point.
Do you know what a power of 10 is?
\(\displaystyle 10^0 = 1\ and\ n \ge 1 \implies 10^n = 10 * 10^{n - 1}.\)
\(\displaystyle So\ 10^0 = 1,\ 10^1 = 10 * 1 = 10,\ 10^2 = 10 * 10 = 100,\ 10^3 = 10 * 100 = 1,000\ etc.\)
The powers of 10 are easy to remember because the nth power of 10 is just 1 followed by n zeroes.
If you count the number of digits to the right of the decimal point, that is the power of 10 to use. In 3.375 there are 3 digits to the right of the decimal so you want the denominator to be 10 to the third power = 1000 (1 followed by three zeroes). And the numerator is the number without a decimal point.
\(\displaystyle 3.375 = \dfrac{3,375}{1,000}.\)
