In the supermarket you want to buy sweets with your pocket money of 20€ and of course you immediately throw sour gummy bears for 3.95€, chocolate for 4.45€, chips for 2.63€ and a huge pack of «colorful mix» for 6.78€ in the shopping trolley. But is the €20 note you have in your pocket enough for that?
In everyday life, we encounter such crooked and complicated numbers that are no longer easy to calculate in our heads. In order to be able to calculate in the supermarket whether your pocket money is sufficient in the end, you need the rough calculation.
Definition Rough calculation
But what is rollover actually?
Under the rollover this is understood in mathematics calculating a task using roughly rounded numbers.
If you apply this to your supermarket purchase, you only count those rounded prices together. the rough calculation you can then do it in your head and then you will know whether you have enough money.
You can check whether you have enough pocket money at the end of the article
Rough calculation, rounding and guessing
When you hear the three terms rollover, rounds and treasure, you probably imagine almost the same thing at first. However, there are differences and they are also important. You can therefore go through each term individually below.
You can find more details on this in the individual articles on rounds and guessing.
Estimate
First of all, take a look at what estimating actually means!
That Estimate refers to determining an approximate result of a task based on personal experience or mathematical procedures.
Put more simply, this means that when you estimate, you judge for yourself which number is roughly represented or meant, without counting or arithmetic. There are no rules and no right or wrong.
For example, by looking at this picture, you could estimate the number of people, without counting them of course.
At first glance, an estimate of 1520 would be quite good.
Round
Rounding is a mathematical, concrete process. You can see the exact definition here:
Rounding is the simplification of numbers according to certain rules.
You have already specified a number when rounding, but you simplify it using the socalled rounding rules and are therefore also less precise. For some situations, however, it is sufficient if a number or the result of a calculation is roughly known, for example the number of inhabitants in Germany.
For example, you have the fourdigit number 3641 in front of you and use the rounding rules to represent it as simply as you like. Of course, calculating with the rounded number is then much less precise, but in some situations it is sufficient if the result is only roughly known. Depending on how you round, different numbers can result!
rollover
Here’s a first look at what rollover means!
This is what is meant by rollover in mathematics calculating a task using roughly rounded numbers.
So, rollover goes one step further than rounding. You need the process of rounding and the rounded numbers to be able to do math with them.
In summary this means:
When you roll over, you bring the numbers (by rounding) into a simplified form, which you can then use to complete the task in the head calculate can.
Of course, with these two numbers, it’s hard to pull them apart right off the bat, so the Round first simplified and then easy in the head commonality charged.
Summary – Rough calculation, guessing, rounding
So, the key differences between guess, turn, and rollover are:
 At the Estimate do you judge which number is shown or meant (without calculating or counting!)
 Individual numbers can rounded will
 A rollover is carried out for complicated tasks in order to be able to solve them in your head
Reasons for the rough calculation
Rollover is often perceived as annoying, but it has advantages for everyday calculations:

the rollover gives a reasonably accurate result very quickly

you can do a rough estimate in your head, you don’t need a pen, paper or pocket calculator (this is useful when shopping, for example)

you can use the rollover to check your previously precisely calculated result
So: Estimating is a quick way and good control of your calculation through mental arithmetic.
Rounding as the basis for the rough calculation
Rounding is an essential part of the rough estimate. If you don’t know exactly how to round correctly, you can read the article about rounding again.
Numbers are shown in a significantly simplified form when they are rounded. To show this, you write the socalled between the exact number and the rounded (and therefore less precise) number round sign .
When rounding, it is also extremely important to which digit of a number is rounded. The socalled rounding place is the digit within a number that is either rounded up or down. You should choose them carefully beforehand.
These rounding places are the most common and conceivable for your calculations:
Make laps…1234.5678 thousand1234.5678 hundreds1234.5678 tens1234,5678Integer1234,5678 tenths 1234.5678 hundredths 1234.5678 thousandths
Table 1: Rounding places
Rough calculation instructions
In the rough calculation, you have to carry out the following two steps in succession:
 First you round all the numbers in your arithmetic problem sensibly.
 Then you use these rounded numbers to do the math in your head.
1st step: rounds
First you have to make it clear to which place of the numbers you want to round, for example to hundredths, whole numbers, tens, thousands or similar. Take a closer look at table 1 rounding point from above.
Figure 1: Sample task rollover
Now you just look at the digit after of the place you want to round to.
Figure 2: Rounding point
If that digit is 0, 1, 2, 3, or 4, round down. This means that the original number remains at the rounding point, all digits after that become zeros.
Figure 3: Round off
If the digit is 5, 6, 7, 8, or 9, round up. In this case, the number of the rounding place is increased by one, all digits after that become zeros.
Figure 4: Round up
2nd step: Invoice
You now use the rounded numbers from step 1 for the calculation.
Instead of the exact numbers, you use the rounded numbers and then calculate your problem as normal.
In the example you write 2700 instead of 2738 and 1800 instead of 1792. You then add the two rounded numbers as usual and get a result of 4500.
So your rollover result is 4500. The exact result would have been 4530.
Rough calculations – addition, subtraction, multiplication & division
You can use the rough calculation in all types of calculation according to the instructions above. In the following, take a closer look at the procedure for rolling over in each basic arithmetic operation using an example.
Rough calculation – addition
task
Calculate the result of the sum 435+761.
solution
Step 1:
First, choose a place to which you want to round both numbers. For this calculation, for example, rounding to the nearest ten makes sense. Then do the rounding according to the rounding rules.
Step 2:
Now add the rounded numbers together in your head and get your estimate result.
Rough calculation – subtraction
task
Estimate the subtraction 36841253.
solution
Step 1:
You look for a rounding place again (for example, this time the hundreds), look at the digit directly after this place and round up or down accordingly.
Step 2:
You also proceed in the same way with subtractions. You also use the rounded numbers and subtract them together in your head.
Rough calculation – multiplication
task
Do a rough calculation of the multiplication problem.
solution
Step 1:
Start again by determining the rounding place (e.g. tens this time) and rounding both numbers accordingly. This simplifies the task for you.
Step 2:
Now all you have to do is multiply the two rounded numbers, i.e. take them together.
Especially when multiplying, rough rounding can lead to large inaccuracies in the result.
Rough calculation – division
task
Calculate the result of the following division.
solution
Step 1:
With the known procedure, you round the two quotients to whole numbers (find the rounding point, then look at the digit and round up or down).
Step 2:
The division is often super easy and the result of the calculation is usually sufficiently accurate.
Special case – Rough calculation decimal numbers
As you can see from the example of division, you need the rollover particularly often when you are doing a task with (long) decimals have in front of you. Regardless of the type of calculation, calculating with decimal places is often very tedious and tedious.
A rough calculation can save you a lot of time.
task
roll over
solution
Step 1:
Handling rounding with decimal numbers is particularly important. It is always easiest when you click on one integer round You can also round to tenths, hundredths, thousandths, and so on.
Step 2:
Whole numbers or otherwise rounded decimal numbers are now much better suited for the calculation.
Memory:
Make laps…1,2345Integer1,2345 tenths 1.2345 hundredths 1.2345 thousandths
Examples rough calculation
To check whether you understood the rough calculation, you can do the following exercises.
Task 1
Roughly do the following in your head:
solution
Step 1:
The task is about a rough estimate, i.e. you choose a higher rounding point. This is where the hundreds come in handy.
If you rounded to the tens or hundreds, that’s not wrong either.
Step 2:
You can now complete the calculation with these rounding values.
exercise 2
At the hardware store you buy 4 items for .
Take a moment to decide whether you like the 200€ enough in your wallet.
solution
Step 1:
With these smaller amounts, it’s best to round to whole numbers and get a reasonably accurate result.
Step 2:
Then, of course, you have to add up all four numbers.
Thanks to your rollover, you can rest assured that the €200 in your wallet will be enough.
task 3
For a friend’s birthday, you team up and buy a present. You are 21 people and wanted him a vacation trip worth 1198€ give a gift.
Briefly estimate how much each individual would have to pay.
solution
Step 1:
Here it is up to you to find a suitable rounding point. It is best to take a close look at the numbers, then you will see that it makes sense to round to the tens.
Step 2:
Now, to find out how much each individual has to pay, divide the total by the number of people who…