# Arithmetic issue

#### Leoninja

##### New member
Hi, I am currently studying maths and it's been a good number of years since I've done this. I am working through a books questions and though I found most really easy I am stumped on one question which is.
A coach can carry 48 passengers. How many coaches are needed to carry 1100 passengers? How many seats will be unoccupied?
I understand the division aspect of dividing 1100/48 which my calculator reads 22.9166
I understand the rounding up to 23 but cant seem to work out how many seats will be unoccupied. Any help would be greatly appreciated. Thanks

#### MarkFL

##### Super Moderator
Staff member
Hello and welcome to FMH!

What is the difference between 23 times 48 and 1100? This will be the number of unoccupied seats.

Thank you.

#### Jomo

##### Elite Member
Division is repeated subtraction. Start with 1100 and keep subtracting 48 until you have less than 48 remaining. According to your work you will have to subtract 48, 22 times. What remains will go onto the 23rd bus. Can you know figure out how many seats will be empty on the last bus?

#### pka

##### Elite Member
I am stumped on one question which is. A coach can carry 48 passengers. How many coaches are needed to carry 1100 passengers? How many seats will be unoccupied?
Look at what one can do with a free web resource. SEE HERE
The lesson here is: All the necessary computing power is freely available but is useless unless one knows how to setup the calculation.

#### HallsofIvy

##### Elite Member
But Wolfram Alpha didn't give you that formula, did it?

Leoninja, you say "I understand the division aspect of dividing 1100/48 which my calculator reads 22.9166
I understand the rounding up to 23 but cant seem to work out how many seats will be unoccupied."
Yes, you will need 23 busses. The excess is in that difference 23- 22.9166= 0.0834. Multiply that by the 48 you just multiplied by to get the "remainder": 0.0834(48)= 4. There will be four seats left empty.

#### Mr. Bland

##### Junior Member
The excess is in that difference 23- 22.9166= 0.0834. Multiply that by the 48 you just multiplied by to get the "remainder": 0.0834(48)= 4.
Apologies since this isn't in the realm of arithmetic but rather computer science, but I don't recommend this specific approach for a very important reason...

Often times when working with calculators you'll have a repeating or infinite result (as is the case here) and the limited precision of the computer may well give you the wrong answer after multiple operations due to rounding. More elaborate calculators will consider the entire input expression, but by the time you have 22.9166666... as in this example, the damage has already been done.

In order to circumvent the potential for rounding errors, one should use an algorithm that avoids forcing the computer to round, as much as possible. @MarkFL gave a good suggestion that isn't subject to precision rounding: multiply the integer quotient of 1100 / 48 (which is 22) by 48, then subtract the result from 1100 to find the remainder.

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