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Polynomials

Question

Wired Faculty App

Write the following in decimal form and say what kind of decimal expansion each has:

$3 over 13$

Solution

3 over 13

13 space right parenthesis space 3.00000000000 space left parenthesis 0.23076923079...... space space space space bottom enclose 26 space end enclose space space space space space 40 space space space space space bottom enclose space 39 thin space space space end enclose space space space space space space 100 space space space space space space space bottom enclose thin space thin space space 91 thin space space space end enclose space space space space space space space space 90 space space space space space space thin space bottom enclose thin space space 78 space space space thin space thin space end enclose space space space space space space space space space space space 120 space space space space space space space space space bottom enclose space space space 117 space space space end enclose space space space space space space space space space space space space space space 30 space space space space space space space space space space space space bottom enclose space space 26 space space space space end enclose space space space space space space space space space space space space space space space space space space 40 space space space space space space space space space space space space space space space bottom enclose space space 39 space space space space end enclose space space space space space space space space space space space space space space space space space space space 100 space space space space space space space space space space space space space space space space space bottom enclose space space space space 91 space space space end enclose space space space space space space space space space space space space space space space space space space space space space 90 space space space space space space space space space space space space space space space space space space bottom enclose space space space 78 space space space end enclose space space space space space space space space space space space space space space space space space space space space 120 space space space space space space space space space space space space space space space space space space space bottom enclose space 117 space space end enclose space space space space space space space space space space space space space space space space space space space space space space space 3 therefore space space 3 over 13 equals space 0.230769230769 space...... space equals space 0. top enclose 230769

The decimal expansion is non-terminating repeating.

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Find two rational numbers between 0.1 and 0.2.

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