1 ÷ 9 = 0.11111

The 1 continues.

So total paint used

= 7.4 l + 0.11111.... l

= 7.5111111.... l

= 7.511 l (3 decimal places)


Alternatively,

Change them to the same denominator.

Common multiple of 9 and 5 is :
9 x 5 = 45

7 2/5 l = 7 18/45 l
(Multiplying both numerator and denominator by 9)

1/9 l = 5/45 l

(Multiplying both numerator and denominator by 5)



Total paint used

= 7 18/45 l + 5/45 l
= 7 23/45 l

now, 23/45 = 0.51111....

So 7 23/45 l = 7.511111....
≈ 7.511 l (3 decimal places)


To be safe , always round off to 3 decimal places at the final step only, to avoid truncation errors.

1/9 = 0.111 ... = 0.111 (to 3 d. p.)

total amt of paint
= 7.4 + 0.111
= 7.511 L


...

Thank you very much

Welcome.

Here's an example of truncation error :


1/12 + 4/7
= 7/84 + 48/84
= 55/84

55/84
= 55 ÷ 84
≈ 0.654761905
= 0.655 (3 decimal places)


Now, if you found them separately and rounded off first for each number,

1/12
≈ 0.0833333333
= 0.083 (3 decimal places)

4/7
≈ 0.571428571
= 0.571 (3 decimal places)


0.571 + 0.083 = 0.654

You would arrive at the incorrect answer 0.654 instead of 0.655 due to rounding off too early.

Well noted with thanks

Hi I would like to have your advise, the question is to round off to 3 decimal places, therefore, the answer is 7.511 or 7.510?

7.511. you always look at the digit after the required number of places to determine how to round it.

In this case, 1/9 + 7.4

= 7.5111111.... Where the 1 is recurring.and goes on.

For 3 decimal places, you look at the 4th decimal place to determine.

5-9, you round up. 0-4, you round down.

The fourth decimal place is a 1, so you round down since it's below 5.

So you round down to 7.511


Another example :


8.634469

The 4th decimal place here is a 4, which is below 5. So round down to 8.634.



Another example:

0.137723

The 4th decimal place here is 7, higher than 5. So round up to 0.138

Well noted with thanks

Welcome. Refer to the edited explanation above.

Thank you very much for your explanation, now I understand already.

Great. Feel free to ask if you have other doubts