Decimals to fractions

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Lauren Richards

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From users who are members of Transition to university :

Chris Graham	said	Ready to use	7 years, 8 months ago
Lauren Richards	said	Needs to be tested	7 years, 8 months ago
Hannah Aldous	said	Has some problems	7 years, 8 months ago
Vicky Hall	said	Has some problems	7 years, 8 months ago
Elliott Fletcher	said	Has some problems	7 years, 8 months ago

History

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Chris Graham 7 years, 8 months ago

Gave some feedback: Ready to use

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Chris Graham commented 7 years, 8 months ago

I fixed the spacing around the = in b)(ii). Otherwise I think this is good.

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Lauren Richards 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Hannah Aldous commented 7 years, 8 months ago

question looks good, just a few little things

question b only has one part so i is unnecessary (same in advice)

advice for parts a, c and d when you do your subtraction make sure it is clear that you are subtracting the whole equation as it looks like you are just making your left hand side negative at the moment

text on advice for a iv is centred whereas the rest of the advice isn't

text for the advice of part c is centred too

part c advice needs a full stop after x= recurring number, before 'By multiplying...'

for your advice for part c maybe include the fact that you are doing the subtraction to remove the recurring numbers

the line beginning 'From this...' continues off the page so can not be read, perhaps because it is in LaTeX

I'd put a space between your final fraction and 'in it's fractional form

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Hannah Aldous 7 years, 8 months ago

Gave some feedback: Has some problems

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Lauren Richards 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Chris Graham commented 7 years, 8 months ago

The student will want to submit each part individually, and for this reason I would split this into two questions.

I have removed the full stops after the fractions. They were not really necessary and their vertical alignment, next to the fraction bar, was awkward.

In (a), clearly (iii) is the toughest. I think I'd swap it for (iv) to give a more logical progression in difficulty.

Where you have \$\displaystyle... you can enclose maths in \[ \] with the same effect.

You also have some centred text in the advice. Note that using\[ \] will centre the maths without the need to centre using the formatting tools.

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Chris Graham 7 years, 8 months ago

Gave some feedback: Has some problems

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Lauren Richards 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Chris Graham commented 7 years, 8 months ago

Hi Lauren, I guess this was after we sorted the other bits on Friday. It appears as though this could be due to floating point precision, such that f2 is not considered a precise integer for the purpose of obtaining the gcd. I have added precround(...,0) to the definition of f2 and I think that this has solved it.

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Lauren Richards commented 7 years, 8 months ago

Everything is fixed now EXCEPT part b)i) STILL does not simplify properly for some unknown reason. It gave 342/1000 as that instead of 171/500 and another time 302/1000 instead of 151/500 and again another time 416/1000 instead of 52/125.

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Lauren Richards 7 years, 8 months ago

Gave some feedback: Has some problems

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Chris Graham commented 7 years, 8 months ago

Hi Lauren, you currently have amissing answer(s) for your gaps. If you can sort that and I'll also come and see you.

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Lauren Richards commented 7 years, 8 months ago

Explanation for "Doesn't work":

The problems with this question are in part b) - part a) is mostly fine.

In part a), I am slightly unhappy about it the apparent impossibility of aligning whilst having an underline. I have a subtraction in part a) and wanted the answer to the subtraction directly underneath the subtraction with an underline separating it but I couldn't get it to work so I now have it not underlined and separated but still aligned.

The big problems are in both sections of part b).

b)i) - The unsimplified fraction does not simplify properly using either gcd or the \simplify command and I cannot for the life of me work out why not. Vicky previously thought the problem was that the numerator and denominator of the fraction were not variables but I have made them so and it still will not 1) identify the correct gcd nor 2) simplify properly. For instance, on the last run it said that with a fraction of 700/1000, 700 and 1000 had a gcd of 1 and therefore the fraction could not be simplified. It's very strange though, sometimes it works and sometimes it doesn't. It is therefore difficult to set the correct answer as there is no predicting which answer itself has calculated.

b)ii) - I have had to create a number using individual variables which is causing problems, e.g. variable a = 1, variable b = 2, variable c = 3 and the full number = 123. Everything is fine up until the end where there is a fraction that needs to be simplified where 123 is the numerator. Numbas obviously won't recognise (1)(2)(3) as 123 so I don't know how to get around this. I could ask the students to just not simplify their answer which gets rid of the problem but Vicky and I both agree that is not best practice.

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Lauren Richards 7 years, 8 months ago

Gave some feedback: Doesn't work

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Lauren Richards commented 7 years, 8 months ago

Vicky had a look at this question but it is still problematic.

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Lauren Richards commented 7 years, 8 months ago

Having a few issues with this question and need a bit of help.

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Vicky Hall 7 years, 8 months ago

Gave some feedback: Has some problems

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Vicky Hall commented 7 years, 8 months ago

I think this should be called 'converting decimals to fractions'. Do you have or are you going to make another question on converting fractions to decimals?

The numbers are very large in part b) of the questions. My first fraction was $\displaystyle\frac{681}{10000}$ and my second was $\displaystyle\frac{4365}{999}$ . I can see fairly easily that $\displaystyle\frac{681}{10000}$ has no common factor but I had to check with my calculator if $3$ was a factor of $4365$ . To fix this, I would reduce the decimal places, so perhaps make the non-recurring decimal $2$ decimal places long, and have the recurring decimal repeat after either $1$ or $2$ decimal places.

Make sure all numbers in the advice are in Latex. In the working for the recurring decimals, it would look much neater to have the $=$ aligned in the subtraction.

I have fixed the notation issue for the recurring decimal in part a).

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Lauren Richards commented 7 years, 8 months ago

I totally agree with Elliott's feedback about notation of recurring decimals but I can't seem to make it work when the recurring decimal is a variable.

Also, in some instances, weirdly, simplify doesn't seem to be working for some of the final answers.

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Lauren Richards 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Elliott Fletcher commented 7 years, 8 months ago

This all looks pretty good, i just have a few suggestions.

Main Parts

a) iii) For a recurring decimal, you could use a handy piece of notation to avoid writing something like 0.6666...

using 0.\dot{6}, you can write the 6 with a dot above it which is the common notation for a recurring decimal. If you do want to use this i would also put a note in the statement saying 0.\dot{6} means 0.666...

Advice

On the first line you say "to convert a fraction into a decimal" whereas this should be "to convert a decimal into a fraction". I also think in this opening paragraph that you should say that you are multiplying the numerator and the denominator of this fraction by 10 instead of just saying that you multiply the whole fraction by 10.

a) iii) I don't think this is really enough of an explanation for how you convert a recurring decimal to fraction. I think there is actually a different method for converting recurring decimals to fractions, see the following link: http://studymaths.co.uk/topics/convertingRecurringDecimalsToFractions.php

a) iv) you haven't entered the decimal that you are converting to a fraction underneath the iv) here as you have with the other questions.

Otherwise, i think this is a good question!

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Elliott Fletcher 7 years, 8 months ago

Gave some feedback: Has some problems

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Lauren Richards 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Lauren Richards 7 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Decimals to fractions	Ready to use	Lauren Richards	20/11/2019 14:47
J. Richard's copy of Decimals to fractions	Ready to use	J. Richard Snape	05/12/2022 15:24
Dezimalzahlen in Bruchzahlen umwandeln	Ready to use	Ulrich Görtz	17/11/2024 18:33

There are 16 other versions that do you not have access to.

Question statement

Fractions can be equivalently represented as decimals and vice versa. One form may be more useful in a context than another and it is useful to practise how to change between them.

Have a go at these questions involving fractions and decimals, remembering to write your answer in its simplest form.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	0.7
b	number	0.25
c	integer	6
d	number	0.4
b_	number	25
b_coprime	number	1
d_coprime	number	2
answer	integer	54
cround	rational	2

			Name	Type	Generated Value

f	number	0.346
f2	number	346
mygcd	number	2
h	integer	4
j	integer	6
k	integer	7
f3	number	173
f4	number	500
f1000	integer	1000
numerator	integer	463
g	integer	99
gcd1	number	1
numerator_coprime	number	463
g_coprime	number	99

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.1,0.3,0.7,0.9)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

0.7

→ Used by:

Advice
"Part a)" - prompt
"Part a)" → "Gap 0." - Minimum accepted value
"Part a)" → "Gap 0." - Maximum accepted value

Parts

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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Express these common decimals as their fraction equivalent.

$\var{a}=$ Gap 0. Gap 1.

ii)

$\var{b}=$ Gap 2. Gap 3.

iii)

$\var{d}=$ Gap 6. Gap 7.

iv)

$0.\dot{\var{c}}=$ Gap 4. Gap 5.

Advice

a)

To convert a decimal into a fraction, firstly place the decimal over $1$ as a fraction, and then multiply both the numerator and denominator by $10$ for however many decimal places the decimal has. For example, if the decimal was $0.1$ , you would multiply the fraction by $10$ as there is one decimal place. If the decimal was $0.01$ , you would multiply it by $100$ , as there are two decimal places.

$\var{a}$

$\frac{\var{a}}{1}\times\frac{10}{10}=\frac{\var{10a}}{10}\text{.}$

ii)

$\var{b}$

$\frac{\var{b}}{1}\times\frac{100}{100}=\frac{\var{100b}}{100}=\simplify{{100b}/{100}}\text{.}$

iii)

$\var{d}$

$\frac{\var{d}}{1}\times\frac{10}{10}=\frac{\var{10d}}{10}=\simplify{{10d}/{10}}\text{.}$

iv)

$0.\dot{\var{c}}$

To convert a recurring decimal to a fraction, the first step is to set up a simple equation where

$x=0.\dot{\var{c}}\text{.}$

By multiplying both sides by $10$ , we can gain another simple equation where

$10x=\var{c}.\dot{\var{c}}\text{.}$

By subtracting one equation from the other, we can find the fraction equivalent of the recurring decimal.

$\begin{align} &&\var{c}.\dot{\var{c}}&={10}x\\ -&&{0.\dot{\var{c}}}&=x\\ &&\overline{\qquad} & \overline{\qquad}\\ &&{\var{c}}&=9x\\ \\ &&\frac{\var{c}}{9}&=x \end{align}$

$\displaystyle\frac{\var{c}}{9}$ simplifies to $\simplify{{{c}}/{9}}$ by dividing by $3$ and therefore, $0.\dot{\var{c}}=\simplify{{{c}}/{9}}$ in its fractional form.}

b)

$\displaystyle\var{f}$

$\var{f}\times\frac{\var{f1000}}{\var{f1000}}=\frac{\var{f2}}{\var{f1000}}\text{.}$

From this, we can look to see if we can cancel down the fraction by finding the highest common divisor between the numerator and denominator. This is $\var{mygcd}$ .

Therefore, it is not possible to simplify the answer any further and the final answer is

Simplifying by this amount gives the final answer

$\frac{\var{f3}}{\var{f4}}.$

c)

$\var{h}.\dot{\var{j}}\dot{\var{k}}.$

To convert a recurring decimal to a fraction, the first step is to set up a simple equation where,

$x=\var{h}.\dot{\var{j}}\dot{\var{k}}.$

By multiplying both sides by $100$ to isolate the recurring section on the left hand side of the decimal point, we can gain another simple equation

$100x=\var{h}\var{j}\var{k}.\dot{\var{j}}\dot{\var{k}}.$

Now that we have two equations in terms of $x$ , we can subtract one from the other and solve to get a value of $x$ .

$\begin{align} &&\var{h}\var{j}\var{k}.\dot{\var{j}}\dot{\var{k}}&=100x\\ -&&\var{h}.\dot{\var{j}}\dot{\var{k}}&=x\\ &&\overline{\qquad} & \overline{\qquad} \\ &&{{\var{h}}\var{j}\var{k-h}}&=99x\\ \\ &&\frac{\var{numerator}}{\var{g}}&=x\text{.}\\ \end{align}$

From this, we should look to see if it is possible to simplify by finding the greatest common divisor of the numerator and the denominator. The greatest common divisor is $\var{gcd1 }.$

Therefore, it is not possible to simplify and so

Simplifying by this value gives the fraction $\displaystyle\simplify{{{numerator}}/{g}}$ and so

$\begin{align} \var{h}.\dot{\var{j}}\dot{\var{k}}=\simplify{{{numerator}}/{g}}\text{ in its fractional form.}\\ \end{align}$

Give a worked solution to the whole question.

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Elliott Fletcher 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Hannah Aldous commented 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Chris Graham 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Lauren Richards commented 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Chris Graham commented 7 years, 8 months ago

Lauren Richards commented 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Lauren Richards commented 7 years, 8 months ago

Lauren Richards commented 7 years, 8 months ago

Vicky Hall 7 years, 8 months ago

Vicky Hall commented 7 years, 8 months ago

Lauren Richards commented 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Elliott Fletcher commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

a)

b)

c)

Generated value: `number`