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Holocene
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Somome told me this. So, this is wrong:
[tex]\displaystyle{\frac{1}{3} = 0.\overline{3}}[/tex]
?
[tex]\displaystyle{\frac{1}{3} = 0.\overline{3}}[/tex]
?
Dragonfall said:Sure it can. What you wrote is the decimal form of 1/3.
epkid08 said:Doesn't that go against the definition of a rational number?
epkid08 said:I wasn't talking about using irrational numbers in algebra...
I was saying that a number that can be expressed as a simplified fraction, can also be expressed as a repeating decimal. That's one of the definitions of a rational number.
epkid08 said:Doesn't that go against the definition of a rational number?
HallsofIvy said:No, it doesn't. A rational number is one that can be represented as a fraction. It doesn't mean that it cannot also be represented in other forms also.
epkid08 said:I don't understand your post. You're saying I'm wrong, but you're also agreeing with me?
His comment is entirely explicable due to the complete paucity of content in that post!epkid08 said:Doesn't that go against the definition of a rational number?
This is NOT what you said in your first post, it is impossible to deduce the contents of this post from the first one, so given HoI's oversight, how should he have understood what your first post meant?epkid08 said:I wasn't talking about using irrational numbers in algebra...
I was saying that a number that can be expressed as a simplified fraction, can also be expressed as a repeating decimal. That's one of the definitions of a rational number.
yenchin said:Might be a good idea to quote which ever post you want to reply to...
epkid08 said:Who are you talking to? how ironic
uman said:This is off-topic, but I've always wondered why many people who refuse to believe that 1 = 0.9... readily believe that 1/3 = 0.3...
Ignea_unda said:Please clarify that 1 = 0.9...
I could see if you are rounding but I do not see those to be equal by definition.
Reminds me of a thread I once posted where I had to describe the series of 0.3,0.33,0.333,0.333, ... and all I needed to do was to write it out as a geometric progressionsketchtrack said:Reminds me of 1/2+1/4+1/8+1/16+1/32...=1
Ignea_unda said:Please clarify that 1 = 0.9...
I could see if you are rounding but I do not see those to be equal by definition.
When a number cannot be expressed in decimal form, it means that it cannot be written as a finite number of digits after the decimal point. In other words, there is no way to represent the number as a decimal with a definite number of digits.
This is because the decimal system is based on powers of 10, while 1/3 is a repeating decimal with a base of 3. Therefore, it cannot be accurately represented in the decimal system without an infinite number of digits.
1/3 is usually represented as a fraction or as a decimal approximation, such as 0.333... or 0.33. However, these representations are not exact and are only approximations of the true value of 1/3.
No, 1/3 is still a valid number and has the same value as any other number. It is simply not possible to express it in decimal form without using an infinite number of digits.
Yes, there are many other numbers that cannot be accurately represented in decimal form, such as 1/7, 1/9, and √2. These numbers are known as irrational numbers and have an infinite number of non-repeating digits after the decimal point.