explain how you can tell by looking at a decimal whether it will convert into a proper fraction or an improper fraction

Question

explain how you can tell by looking at a decimal whether it will convert into a proper fraction or an improper fraction.

Answer 1

A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number).

 

An Improper Fraction has a top number larger than (or equal to) the bottom number.

 

So, if the decimal value has 0 before the decimal point, it may (because not all decimals can convert) be a proper fraction.

If the decimal value has anything other than 0 before the decimal point, it may be an improper fraction.

 

TMI:

 

To convert a non-repeating decimal to a fraction:  put the numerator over 1000.. with the proper number of zeros and reduce it.    For example,  0.75  is  75/100  is 3/4.

 

To convert a repeating decimal to a fraction:  If all the digits are repeating. put the repeating part over as many 9's as there are digits that repeat.   For example,  0.108108108...  is 108/999 = 4/37.

 

To convert a decimal with some non-repeating digits then repeating digits (learn this later), you may solve some simultaneous linear equations.

 

Answer 2

Decimals have significant digits after the decimal point.  If there is a pattern, such that these significant digits repeat over and over, then we can convert to any kind of fraction.  However, if the significant digits appear at random without any sequence, then we have irrational numbers. Here are some examples of decimals that can be converted to a fraction.

 

 

0.10

 

0.2020

 

0.25

 

0.50

 

0.75

 

0.3333333

 

0.6666666

 

0.875

 

0.125

Answer 3

if the decimal is less than one will convert into a proper fraction. Examples 1/2 =0.5, 1/8 =0.125

 

if a decimal is greater than or equal to one will convert into a improper fraction. Example 11/5 =2.2, the resultan fraction can also be converted into a mixed fraction 2 1/5.