If the digit we want to discard is 5, but there are no significant digits behind it, then the last stored digit remains unchanged, if it is even, and if it is odd, it increases by one. Example 1: there is a number 42.85, we round it to tenths. We discard the number 5, a, because after it there are no significant digits, and the last stored digit 8 is even, then it remains unchanged. That is, we get the number 42.8.

Example 2: the number 42.35 is rounded to tenths. The discarded digit 5 does not have significant digits, but the last stored digit 3 is odd, then it accordingly increases by one and becomes even. We get 42.4.

## Round number

This mathematical action is carried out according to certain rules.

But for each set of numbers they are different. It is noted that integers and decimal fractions can be rounded.

But with ordinary fractions, the action is not performed.

First, they must be converted to decimal fractions, and then proceed to the procedure in the necessary context.

The rules for approximating values are as follows:

- for integers - replacement of the digits following the rounded ones with zeros,
- for decimal fractions - discarding all numbers that are behind a rounded digit.

For example, rounding 303,434 to thousands, you need to replace hundreds, tens and ones with zeros, that is, 303,000. In decimal fractions, 3.3333 **rounding to tens**x, just discard all subsequent digits and get the result 3.3.

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## Exact rules for rounding numbers

When rounding decimal fractions, it’s not enough just to drop the numbers after the rounding digit. You can verify this with an example. If the store bought 2 kg of 150 g of sweets, then they say that about 2 kg of sweets were purchased. If the weight is 2 kg 850 g, then round up, that is, about 3 kg. That is, it is seen that sometimes the rounded discharge is changed. When and how they do it, they can answer the exact rules:

- If the number 0, 1, 2, 3 or 4 follows after the rounding digit, then the rounding one is left unchanged, and all subsequent digits are discarded.
- If the number 5, 6, 7, 8, or 9 follows the rounding digit, then the rounding one is increased by one, and all subsequent digits are also discarded.

For example, how to correctly fraction **7.41 approximate to units**. The figure that follows the digit is determined. In this case, it is 4. Therefore, according to the rule, the number 7 is left unchanged, and the numbers 4 and 1 are discarded. That is, we get 7.

If the fraction 7.62 is rounded, then the units are followed by the number 6. According to the rule, 7 must be increased by 1, and the numbers 6 and 2 should be discarded. That is, the result is 8.

The examples presented show how to round decimals to units.

### Approximation to whole

It is noted that rounding to units can be done in exactly the same way as to integers. The principle is the same. Let us dwell in more detail on the rounding of decimal fractions to a certain category in the whole part of the fraction. Let us present an example of approximation of 756.247 to tens. In the tenth place, there is the number 5. After the rounding digit, the number 6 follows. Therefore, according to the rules, it is necessary to fulfill **next steps**:

- rounding up dozens per unit,
- in the category of units, the number 6 is replaced by zero,
- digits in the fractional part of the number are discarded,
- the result is 760.

Let us pay attention to some values in which the process of mathematical rounding to the nearest integer by rules does not reflect an objective picture. If we take the fraction 8,499, then, transforming it according to the rule, we get 8.

But in fact this is not entirely true. If you round off bitwise to integers, then first we get 8.5, and then we discard 5 after the decimal point, and we round up.

We get 9, which, in principle, does not suck for sure. That is, in such values the error is significant. Therefore, we evaluate the task and, if the situation allows, it is better to use the value of 8.5.

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### Approaching to tenths

How to round to tenths, to hundredths, to thousandths? The operation is carried out according to the same rules as before the whole. The main task is to correctly determine the rounded digit and the sign that follows it.

For example, a fraction of 6.7864 when bringing:

- to tenths becomes equal to 6.8,
- to hundredths - 6.79,
- if rounded to thousandths, they get 6.786.

Note! Ignorance of these rules is very successfully used by marketers. In stores, observing the price tag with the number 5.99, the majority of buyers perceive a price equal to 5. In reality, the price of the goods is almost 6.

Math learn to round numbers

Rules for rounding numbers to tenths

The priorities of the ability to perform such mathematical operations can be given quite a lot. It is important to learn how to correctly assess the situation, set a goal, and the result will come immediately.

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