How do you write a decimal in expanded form as a fraction?

Answer 1

It is quite simple to change a decimal form into a fraction.

Any number , including a decimal can be divided by 1, and multiplied by 1.

Take the decimal .156 for example

first divide it by 1; yields

.156/1

now do some fraction multiplication

(.156/1) x (1000/1000) (note 1000/1000 =1, so mult of the decimal dosen't change its value)

this yields 156/1000 , so .156 = 156 thousandths

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A more interesting problem arises from trying to expand a repeating decimal

example .175175175175175............and so on

Let X =.175175175175175..........

then 1000X=175.175175175......... (note the decimal place after 175)

so 1000X-1X=999X = 175

then dividing by 999 gives

x=175/999

so .175175175.........=175/999 as a fraction.