Decimal to Fraction
Intro: Decimal to Fraction
Do you need to convert a decimal to a fraction or back the other way?
This will explain how to convert:
Decimals to Fractions
AND
Fractions back to Decimals
This will explain how to convert:
Decimals to Fractions
AND
Fractions back to Decimals
STEP 1: The Conversion
To convert a decimal to a fraction you need to know what each place in a decimal equals.
see the chart below
To make it easier think of it this way:
the ones place is x/1, place just to the right of the decimal is x/10, the next place to the right is x/100, etc...
For each place the you move to the right of the decimal add another zero (0) to the denominator.
so 0.5 = 5/10, 0.006 = 6/1000, 0.0004 = 4/10000
see the chart below
To make it easier think of it this way:
the ones place is x/1, place just to the right of the decimal is x/10, the next place to the right is x/100, etc...
For each place the you move to the right of the decimal add another zero (0) to the denominator.
so 0.5 = 5/10, 0.006 = 6/1000, 0.0004 = 4/10000
STEP 2: What About a Decimal With More Than One Numeral???
If the decimal has more than one numeral in it it's still just as easy to turn into a fraction.
For example: If the decimal is 0.0023 you would go to the largest place (the 4th place in this case) and use that as your denominator (4th place= x/10000). The numerator is the numerals in the decimal(23 in this case). So for the decimal 0.0023, the fraction would be 23/10000.
For example: If the decimal is 0.0023 you would go to the largest place (the 4th place in this case) and use that as your denominator (4th place= x/10000). The numerator is the numerals in the decimal(23 in this case). So for the decimal 0.0023, the fraction would be 23/10000.
STEP 3: Simplifying a Fraction
To simplify a fraction you first need to find the Greatest Common Factor (GCF) of both the numerator and the denominator. You then divide the numerator by the GCF and the denominator by the GCF.
if you need help with the GCF see step 1 and 2 of this instructable by Phoenixsong.
Ex: The GCD of 60/140 is 20. 60/2=3 and 140/20=7. The new simplified fraction is 3/7.
if you need help with the GCF see step 1 and 2 of this instructable by Phoenixsong.
Ex: The GCD of 60/140 is 20. 60/2=3 and 140/20=7. The new simplified fraction is 3/7.
STEP 4: Fraction Back to a Decimal
The fraction a/b translated into english would by a divided by b.
So to find the equation for converting two-thirds (2/3) into a decimal. You would take a(2) and divide it by b(3).
(If you don't know how to divide look at this instructable by TechnoGeek95.)
2/3=0.66666...
So to find the equation for converting two-thirds (2/3) into a decimal. You would take a(2) and divide it by b(3).
(If you don't know how to divide look at this instructable by TechnoGeek95.)
2/3=0.66666...
STEP 5: Types of Decimals
2/3=0.66666...
This is called a repeating decimal it goes on forever repeating the same digits over and over.
ex: 0.66666...., 0.123123123..., 0.104710471047...
to simplify this number you have two options.
1)put a line over the repeating digits
2)round the decimal off
Another type of decimal is a terminating decimal.
A terminating decimal is a decimal that stops.
ex: 1/8 = 0.125, 1/50 =0.02, 1/32 = 0.03125
The third type of decimal is a irrational decimal.
An irrational decimal is one that does not terminate or repeat.
ex: pi, the square root of 2, any other non-perfect square roots
To simplify this number you can:
1) Round it off to whatever place you choose.
This is called a repeating decimal it goes on forever repeating the same digits over and over.
ex: 0.66666...., 0.123123123..., 0.104710471047...
to simplify this number you have two options.
1)put a line over the repeating digits
2)round the decimal off
Another type of decimal is a terminating decimal.
A terminating decimal is a decimal that stops.
ex: 1/8 = 0.125, 1/50 =0.02, 1/32 = 0.03125
The third type of decimal is a irrational decimal.
An irrational decimal is one that does not terminate or repeat.
ex: pi, the square root of 2, any other non-perfect square roots
To simplify this number you can:
1) Round it off to whatever place you choose.
4 Comments
Jack A Lopez 15 years ago
Maybe one of the instructibles elders reading this could comment? I'm just a noob here really.
I would think it would be legal to make edits to your ible up until the deadline of the contest, but that's just a guess. As far as using my suggestions, I hereby give you permission to use whatever intellectual "stuff" I've given you, licence-free, and you don't have to a attribute it to me either.
Also I think maybe I just made that comment to show off a little bit, without the large amount of work of writing a whole instructible myself. That'd probably be the ethical way for me to show off my math smarts.
And of course, while I was trying to be smart the editor screwed up the formating. I was trying to write the denominator is (10n -1), not 10(n-1) followed by a bunch of small superscripted text.
;-)
Jack A Lopez 15 years ago
All repeating fractions have (10n-1) for the denominator, and the repeating part for the numerator, where n is the length of the repeating part.
Example:
0.12871287128712... = 1287/9999 = 13/101
Goodhart 15 years ago
Sure, if you can make is as well organized as this one (also note the first few of Kiteman's Laws ;-)
Goodhart 15 years ago