



 
Hi Ruth, The 0 in the two decimal representations of the numbers have different place values. Below is a place value chart. Below I have written the decimal number 0.645 in the place value chart. Since 6 is in the tenths place it represents $\large \frac{6}{10}.$ Since 4 is in the hundredths place it represents $\large \frac{4}{100}.$ Since 5 is in the thousandths place it represents $\large \frac{5}{1000}.$ Thus \[0.645 = \frac{6}{10} + \frac{4}{100} + \frac{5}{1000}.\] Writing this with a common denominator I get \[0.645 = \frac{6 + 40 + 500}{1000} = \frac{645}{1000}.\] This fraction can be simplified. In a similar fashion \[0.108 = \frac{1 + 0 + 800}{1000} = \frac{108}{1000}.\] This fraction can also be simplified. I hope this helps,  


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