It is required to find a rational number which is equal to the recurring number 0.737373...
(a) Given that x = 0.737373..., find the value of 100x - x
(b) hence express 0.737373... in the form a/b, where a and b are integers
For (a), what form do I leave the answer in?
and for (b) how do I make use of the answer from (a)?
I understand that the above are basic questions but my teacher told us that it's because over the years students are getting more and more "exam-smart" so the determining factor lies in whether the students understand the meaning of evaluate and give the answer in exact form, etc. So I would like to know if anyone here knows how I should express my answer.
Big thanks to all!
Originally posted by Audi:It is required to find a rational number which is equal to the recurring number 0.737373...
(a) Given that x = 0.737373..., find the value of 100x - x
(b) hence express 0.737373... in the form a/b, where a and b are integers
For (a), what form do I leave the answer in?
and for (b) how do I make use of the answer from (a)?
I understand that the above are basic questions but my teacher told us that it's because over the years students are getting more and more "exam-smart" so the determining factor lies in whether the students understand the meaning of evaluate and give the answer in exact form, etc. So I would like to know if anyone here knows how I should express my answer.
Big thanks to all!
hmm....for (a) I think you can leave the answer as the whole number if you know the trend and what the answer willl eventually be if you have infinite recurring of 0.737373...
that will give 72.9999999927 I think or 73 though strictly following the algebraic formula, 100x-x = 100(0.7373) - 0.7373
or 100 (0.73737373) - 0.737373
you will never ever reach the whole number strictly, but you can give 73.
For (b), 100x-x = b, so x(100-1) = b
so, x = b/99 or 73/99
Originally posted by Audi:It is required to find a rational number which is equal to the recurring number 0.737373...
(a) Given that x = 0.737373..., find the value of 100x - x
(b) hence express 0.737373... in the form a/b, where a and b are integers
For (a), what form do I leave the answer in?
and for (b) how do I make use of the answer from (a)?
I understand that the above are basic questions but my teacher told us that it's because over the years students are getting more and more "exam-smart" so the determining factor lies in whether the students understand the meaning of evaluate and give the answer in exact form, etc. So I would like to know if anyone here knows how I should express my answer.
Big thanks to all!
a)
100(0.737373...)-(0.737373...)
=73.737373... - 0.737373...
= 73 ( it is an exact integer)
b)
Hence we know that 100x - x = 73
99x = 73
x = 73/99
Originally posted by Audi:I understand that the above are basic questions but my teacher told us that it's because over the years students are getting more and more "exam-smart" so the determining factor lies in whether the students understand the meaning of evaluate and give the answer in exact form, etc.
Hi,
There are many key words you often encounter in mathematics exam questions. Please familiarise yourself with these words, and share them with your friends and even your teachers. Thanks!
Some examples of process words (or key words) and their implied meanings are:
1. 'Write down', 'State', 'Give', 'Express/Express briefly', 'List', 'Specify' mean write down without justification, i.e. no working need be shown (although you may include appropriate working if it helps you).
2. 'Find', 'Calculate', 'Determine', 'Simplify', 'Derive', 'Solve', 'Evaluate' 'Transform', 'Expand', 'Factorise', 'Differentiate', 'Integrate' mean work out and show your working, using standard results and techniques.
3. 'Prove', 'Show', 'Deduce', 'Explain', 'Indicate', 'Justify', 'Demonstrate', 'Determine', 'Decide (if, whether ...)', 'Verify', 'Confirm', 'Test', 'Predict', 'Illustrate', 'Identify' mean you must justify each step and provide a convincing argument.
4. 'Assume', 'Consider', 'Suppose', 'Apply', 'Use', 'Define (in terms of ...)', 'Sketch', 'Draw', 'Plot', 'Graph', 'Compile (a table ...)', 'Make (a table, list, ...)' indicate you must answer the question in a particular way indicated by whatever words immediately follow each of these cueing terms.
5. 'Explore', 'Investigate', 'Devise', 'Design', 'Obtain', 'Find', 'Adapt', 'Construct', 'Produce (an algorithm, argument, diagram, ...)', 'Translate (from, into, ...)' indicate doing a mathematical activity and then reporting on the process and result.
Source: Success with Mathematics by Heather Cooke, pp. 49
Thanks!
Cheers,
Wen Shih
Originally posted by Mikethm:a)
100(0.737373...)-(0.737373...)
=73.737373... - 0.737373...
= 73 ( it is an exact integer)
b)
Hence we know that 100x - x = 73
99x = 73
x = 73/99
Hello. How do you know that for (a), it's an exact integer when we do not know when the number stops?
Thanks
Originally posted by Audi:Hello. How do you know that for (a), it's an exact integer when we do not know when the number stops?
Thanks
Two magic words, observation and experience.
Note that they used the word "recurring".