Answers to Decimals Exercise 1.1

1. 4,5    
2. 3,6
3. 2,25    
4. 0,5
5. 0,6    
6. 0,375
7. 0,625
8. 0,875
9. 0,33333… Never-ending!  
10. 3,1428571… Never-ending!

These last 2 are very interesting decimals.  We call them recurring decimals.  You will see that the answer to 9 is 0,3333333…. And it doesn’t matter how long you go on dividing by 3, you will just keep repeating the same process.  We say that the decimal goes on repeating itself to ‘infinity’.  In other words, we could go on and on dividing for our lifetimes and get someone else to go on after we had died and they could get someone else to go on for all of time, and the number would just keep repeating itself for ever and ever.                                                

We write this number like this:

 The ‘dot’ on top of the 3 means the 3 is repeated to infinity.   

Now if we look at exercise 10, it is even more interesting.  Here a whole group of numbers will carry on repeating to Infinity.  One way of indicating this is to write the number with dots on top of all the repeated numbers, so our number 3,1428571……. in which the whole group of numbers 1428571 is repeated to infinity would be written like this:

  or  

 

Both forms may be used.