MHB Repeated and Nonrepeated Decimals

  • Thread starter Thread starter mathdad
  • Start date Start date
AI Thread Summary
Repeating decimals are rational numbers because they can be expressed as a fraction, such as 0.154 repeating, which equals 154/999. In contrast, non-repeating decimals are irrational, as they cannot be represented as a ratio of integers; an example is the decimal representation of the square root of 2. All decimals fall into either the repeating or non-repeating category, which means not all decimals are rational. This distinction highlights the existence of irrational numbers in mathematics. Understanding these classifications is essential for grasping the nature of numbers in decimal form.
mathdad
Messages
1,280
Reaction score
0
My question concerns repeated and nonrepeated decimals. Are both rational numbers? Can you give an example for each?
 
Mathematics news on Phys.org
RTCNTC said:
My question concerns repeated and nonrepeated decimals. Are both rational numbers? Can you give an example for each?

A repeating decimal number is rational because you can always express such a number as the string of repeating digits over an equal number of 9's (one of the tricks my father taught me as a child). For example, we may write:

$$0.\overline{154}=\frac{154}{999}$$

A non-repeating decimal is irrational since it cannot be expressed as the ratio of one integer to another. $\sqrt{2}$ is an example of a non-repeating decimal.
 
You realize, I hope, that all decimals are either "repeating" or "non-repeating". So if it were true that "all repeated and non-repeated decimals are rational numbers" then there would be no irrational numbers!
 
MarkFL said:
A repeating decimal number is rational because you can always express such a number as the string of repeating digits over an equal number of 9's (one of the tricks my father taught me as a child). For example, we may write:

$$0.\overline{154}=\frac{154}{999}$$

A non-repeating decimal is irrational since it cannot be expressed as the ratio of one integer to another. $\sqrt{2}$ is an example of a non-repeating decimal.

More important information.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

B Can an infinite decimal expansion of a number repeat once?
Replies
15
Views
1K
Difference between terminating and repeating decimals
Replies
8
Views
5K
I On base-b expansion of nonnegative reals
Replies
7
Views
2K
B Does Infinity Times Two Equal Infinity and Other Mathematical Paradoxes?
Replies
7
Views
2K
Insights What Are Numbers?
Replies
13
Views
4K
Why some repeating decimals have nonrepeating part? I think its blasphemy Help
Replies
4
Views
3K
B How to convert a fraction into a repeating decimal
Replies
9
Views
2K
I Decimal Precision - Multiplying, Rounding, and Adding
Replies
8
Views
2K
MHB Converting Decimal to Hexadecimal for Compass Corrections
Replies
1
Views
1K
B Another consequence of Cantor's diagonal argument
Replies
43
Views
5K

Hot Threads

Recent Insights

Back
Top