Decimal Rounding: Learning Math
So, now we will see with you how decimal rounding takes place. In fact, this process is not as complicated as it may seem at first glance. True, some schoolchildren have difficulties with this topic. Let us help them understand our today's question.
Concept of decimal fraction
Before rounding off decimal fractions, we need to clearly understand what we have to deal with. The better we understand this question with you, the easier it will be in the future.
In general, the concept of "decimal fraction" is revealed in the 5th grade of the school. This is a kind of number consisting of an integer part and a fractional, the denominator of which is 10.
In order to clearly understand what is at stake, let's look at an example, and then examine how rounding decimals occurs. This type of record will look like this: 5,26852. If you translate the resulting number into a fraction, you can see the following: 526852/100000. Decimal fractions can be both positive and negative.That's all. Now let's go with you to our problem.
The point is that rounding of decimal fractions (Grade 6), as a rule, occurs in parts. First, they take up the remainder ("tail"), that is, those numbers that are after the comma. Only then can be taken for the whole part.
The first thing that is required of us is to determine the accuracy with which we will round out the decimal fractions. Up to tenths, hundredths, thousandths and so on. Then you have to follow some rules, as well as learn one important point that will definitely help you cope with the task. Let us work with you with a clear example. Take an arbitrary number: 78,9563245. It is on it that we will test with you the rule for rounding decimals. Now we get to know him.
The basic principle that we need to learn is how to replace numbers when rounding. The thing is, it's pretty easy to do. Let's see exactly how.
If you have 0, 1, 2, 3, or 4 as a digit, it is automatically replaced with 0 and discarded. Next, move closer to the integer part and look at the next number.
As soon as the digit in the digit is 5, 6, 7, 8, or 9, you will have to discard this part, and add one to the next one (closest to the integer part). This process must be repeated up to the chosen accuracy of rounding. Let's look at an example with you now. On it everything will look clearer.
So, we start rounding decimals with you. We work with the number 78,9563245. We round it up to the tenth, hundredth and thousandths. Let's try.
To begin with, we discard the whole part. We have 0.9563245. We will continue to work with you with this particular number. Let's start rounding off with thousandths, gradually increasing accuracy.
The number is 0.9563245. Moving towards zero. The first number from the end is 5. This means that we “convert” it to 0, and add 4 to 4. The second digit - 4 + 1 = 5. Hence, we assign a unit to the next sign, and this one is converted to 0.
So far we have worked with you: 0.95632(+1). Rounding up to the thousandth is 3 digits. Let's continue to work with you. 2 + 1 = 3. This figure is less than 5s. So, just replace it with 0 and remove. The next stage is 3-ka. Nothing is added to it. Just replace with 0, since it is less than 5. We did it with you: 0.956.Now you can add the whole part: 78,956.
But our rounding of decimal fractions does not end there. Now you should hold it to the hundredth. To do this, as before, we look at the last digit after the comma - 6. According to the rule, we replace it with 0, and then simply add 1 to the digit to the left of it. We get 78.96. Rounding up to tenths here is not very suitable. We get an integer with you. After all, 6-ka will be replaced by 0, the unit will be added to 9, and in the end we get: 78.9(+1). It will turn out 79. That's all. Now you know how to round fractions.