Maths

>

KS3

>

Numbers

>

How do you...

Question
# How do you convert a fraction to a decimal then a rounded decimal into a fraction? Would the answer be different?

1 year ago

·

6 Replies

·

1010 views

B

Blair Christiansen

6 Answers

K

Kinga Brady

You simply have to do the math. 2/3 becomes a decimal if you actually divide 2 by 3. The result will be 0.666, so about 0.67. Now, if you want to go the opposite way, knowing the place values becomes important. 0.1 is actually 1/10, and 0.12 is actually 12/100. So, 0.67 is 67/100. That is very close to 2/3.

M

Mohammed Kibriah

Using the bus stop method you can convert the fraction into a decimal by diving the numerator (top number) by the denominator (the bottom number). Divide the top number by 1 and then multiply the decimal to make it a full number, for example if you have 0.1/1 multiply both the numerator and denominator by 10 to get 1/10. Afterwards if you can simplify further do so.

M

Maribel Ganeb

To convert a fraction into decimal you just have to divide it or initially, you must change it to lowest term the divide it to get its decimal point. say 5/15 so it is 1/3 so 1/3= 0.33.

In the of a rounded decimal say.. 0.736 to round it off.. it will become 0.74.. so when converting into fraction, there will two digits on the denominator so it will become. 74/100, so it will 37/50.. where as if it is not rounded off.. it will becom 736/1000 so it will be 184/250= 92/125..

therefore , there will be a different answer in terms of the fraction conversion when it is rounded off..

A

Aksaaran Selvanathan

To convert a fraction into a decimal, the denominator(bottom number) must not be a prime number. If the number IS convertible, for example, 1/16 to a decimal, you must divide 100 by the denominator, which gives you 6.25. Then you must add the two 0's from the 100 onto this, to make 0.0625. If this was rounded to 2 decimal places, it would become 0.063, which would be as a fraction, 63/1000. So yes, the answer would be different.

A

Alex Staniforth

Let's answer your question using two examples:

A) Converting 3/5 to a decimal with 1.dp and then converting that decimal back into a fraction.

We divide the numerator (3) by the denominator (5).

To do this, we are looking to find how many 5s fit into 3.

Because 5 is larger than 3, the answer is going to be less than 1.

To solve this equation, we multiply out the numerator by 10 which allows us to see how many 5s would fit in 30.

The answer is 6, but remember how we multiplied the numerator by 10 to find out how many 5s would fit into 30?

We now need to undo this by dividing 6 by 10 to find how many 5s would fit into 3.

This gives 0.6 to 1.dp. Therefore 3/5=0.6 to 1.dp.

To convert this decimal into a fraction, we take the decimal (0.6) and put it over its place number (1) to give 0.6/1.

But this isn't tidy and the decimal remains.

Similar to before, we are going to multiply both numerator and denominator by 10 to get whole numbers.

This gets us to 6/10, which is a valid fraction of 0.6 1.dp.

We can do one step better by finding any common multipliers in both numerator and denominator and taking them out.

In this case, the lowest common multiple of 6 and 10 is 2, so we divide 6 and 10 by 2 giving us 3 and 5 respectively.

Our final answer is 3/5.

So in this case, whether the decimal is rounded to 1.dp or 100.dp doesn't impact the conversion. But this is not always the case. Let's have a look at a more tricky example:

B) Converting 7/3 to a decimal with 2.dp and then converting that decimal back into a fraction.

Following the same process as above, we find how many 3s fit into 7.

3 is smaller than 7 so we know we're going to get a decimal answer that reads greater than 1.00.

7 is equal to 6+1 and we know 3x2=6.

This means that 7/3 is equal to 2 and 1/3.

Following the same process as before, we are looking to find how many 3s fit into 1.

3 is larger than 1 so we multiply 1 by 1000 to see how many 3s fit into 1000.

We use 1000 here as we are looking for an answer to 2.dp and need to determine which way to round from the 3rd dp.

3 goes into 1000 333 times with a remainder of 1.

We multiplied the numerator by 1000 and so now need to do the opposite to get our decimal.

333 divided by 1000 is 0.333. We want an answer to 2.dp so we round down to 0.33 as 3 is less than or equal to 5.

From our earlier working, we found that 7/3 was equal to 2 and 1/3. We have now found that 1/3 is equal to 0.33 to 2.dp.

Therefore 7/3 is equal to 2.33 to 2.dp.

We now need to reverse the operation to convert the decimal into a fraction by finding the highest common factor.

First we take the decimal and put it over its place number. 2.33/1

We can multiply both numerator and denominator by 100 to get rid of the decimal to give 233/100.

In this situation there are no more factors left so the simplest way to express 2.33 2.dp as a fraction is 233/100, not 7/3.

While rounding numbers may not seem to matter, they impact the accuracy of your answer.

If you find that a partial answer that you'll use in later operations is a long decimal then make sure to use all of it in your workings.

A

Abbie Smith

To convert a fraction to a decimal: divide the numerator (top of the fraction) by the denominator (bottom of the fraction). This will give the decimal equivalent of the fraction.

3 divided by 4 = 0.75

Think you can help?

More Maths KS3 Questions
##
Need
a KS3
Maths
tutor?

Get started with a free online introductions with an experienced and qualified online tutor on Sherpa.

Find a KS3 Maths Tutor