find a number between 3.24 and 3.241 if there is one. is there is no number between them,explain why not.

the smallest real number that is greater than 2?explain or why not in your own words.

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- Apr 25th 2008, 01:29 PMluzeritoa little help please
find a number between 3.24 and 3.241 if there is one. is there is no number between them,explain why not.

the smallest real number that is greater than 2?explain or why not in your own words. - Apr 25th 2008, 01:31 PMThePerfectHacker
- Apr 25th 2008, 01:57 PMJhevon
- Apr 25th 2008, 02:58 PMMathstud28
- Apr 25th 2008, 03:34 PMxifentoozlerix
If you have two distinct real numbers $\displaystyle x$ and $\displaystyle y$, you can ALWAYS find a number $\displaystyle \frac{x+y}{2}$ where $\displaystyle x<\frac{x+y}{2}<y$. For your example, $\displaystyle 3.24<\frac{3.24+3.241}{2}<3.241 \implies 3.24<3.2405<3.241$.

- Apr 25th 2008, 03:43 PMSoroban
Hello, luzerito!

Quote:

Find a number between 3.24 and 3.241. If not, explain.

Given two different numbers, their__average__is always between them.

For example: .$\displaystyle \frac{3.24 + 3.241}{2} \:=\:3.2405$

. . and: . $\displaystyle 3.2400 < 3.2405 < 3.2410$

Quote:

The smallest real number that is greater than two.

If you say: .$\displaystyle 2\frac{1}{10} = 2.1$ is the smallest,

. . we can say: .$\displaystyle 2\frac{1}{1,\!000} = 2.001$ is smaller,

. . then you can say: .$\displaystyle 2\frac{1}{100,\!000} = 2.00001$ is even smaller . . . etc.