In mathematics, a person has certainly seen number figures followed by a dot. This dot is nothing but a decimal point. This particular expression in a numeric value shows the exact number, not an approximate one.
If you are familiar with fractions, you can certainly understand the logic behind decimals. It is because if a fraction of ½ is to be represented in a numeric value, then, using the decimals, one can describe them by 0.5 in multiple matters.
The decimal number system is a convenient way to represent fractions and an exact number of a given value. If you want to know about the decimal number system, keep reading the upcoming sections for thorough detail.
What are decimals?
Decimals are numeric values where a decimal point separates the whole number from its fractional parts. In mathematics, decimals are used to represent an exact value by replacing approximate figures.
In simple words, decimals are a convenient way to show fractional values. However, decimal values are easier to express and calculate than fractional values. In general, when we talk about decimals, we generally refer to the numeric values that also contain a decimal point. This particular point acts as the identification of the decimal numeric values.
What is a decimal point?
It is easy to identify a decimal numeric value when a decimal point is present. For example- 7.4, 4.12, 0.56, 8.02, and so on are all decimal values as they have a decimal point in them.
This decimal point also signifies that if it were to be removed, then that particular numeric value can be converted to a fractional value. For example – if from the decimal value of 4.12, the decimal point is to be removed, then the whole number value will turn into its fractional value.
4.12 = 412/100
If the value of 412/100 is to be simplified, then the decimal value of 4.12 will result. The same is the case with other numeric values with a decimal point. Removing the decimal point will convert the given numeric value to its fractional representation.
What do you understand by rounding off decimals?
In a decimal value, certain numbers proceed after the decimal point. Even though these numbers have a significant value, it is always less than one. The first digit appearing after a decimal point is termed tenths, and the second number appearing after the decimal point is known as hundredths and so on.
As far as the rounding off decimals is concerned, it is done only to the value appearing after the decimal point. It means in the decimal value of 6.38, only 38 is eligible for the round-off.
On the other hand, it is possible to round off even the whole number that appears before the decimal point. However, one has proved this by rounding off the decimal values first.
Why is it important to round off decimals?
Finding the estimate or approximation is word rounding of implies. Estimation or approximation is a way of determining an estimate or approximate value. This value can then be utilized for any purpose, even if the input data is inaccurate, unreliable, or unpredictable.
On the other hand, the estimated value is functional because it is derived from the most accurate information. Generally, the method involves assessing a value related to a population parameter by using the value of a statistic taken from a sample.
This sample comprises data or information that may be forecasted using various formal and informal methods to determine the spectrum that is most likely to reflect the missing data. Rounding off a decimal value can give the nearest correct value of a numeric expression. Even though it will not be accurate, it will be close to the real numeric figure.
More about the importance of estimation
If the estimate approaches the real result, the computation will be an overestimation. On the other hand, if the estimation falls short of the actual mark, it will be an underestimation.
It shows that approximation theory deals with discovering simpler functions compatible with any complicated process. The approximation theory should also produce helpful estimates and specify the approach of finding predictions in the form of changed bounds for a value that cannot be measured correctly.
How to round off any decimal number?
It is an arithmetic method to round off decimal values which result in the estimated value of a particular number. All the decimal values are rounded off to a specific place after the decimal point. It is done to make them easier to handle and calculate.
Rounding off is a convenient way to avoid a long series of decimal numeric values after the decimal point. Rounding off does not only make it easy to read but also makes it easier to calculate the given numeric value.
How to round off a decimal number to the nearest whole number?
When a person wants to round off a decimal number, there are specific things to consider.
When rounding decimals to the closest whole integer, the tenth digit is checked to see if it is more than five or less than it. The number is rounded up if the tenth digit equals or more than five. However, the number is rounded down if it is less than 5.
If the digit on the tenth decimal value happens to be more than 5, then one is added to the whole number left to the decimal point. After lowering all the numbers to the right after the decimal point, one can write the remaining digits.
One can follow the following rules to round off decimals.
- Round off to estimate the closest whole number in a decimal value.
- The nearest decimal point should also be evaluated to round off a whole number.
- Rounding off decimals up to the second decimal place means rounding off the nearest hundredths.
For example- 7.6
After rounding off – 7.6 becomes 8 (as 6 is greater than 5)
How to round off a decimal number to its nearest tenths?
Rounding off a number to its nearest tenth is the same as a number rounded to its one decimal place. In this case, the numeric value is identified by its 100th place. On the other hand, after rounding off the 100th place, the 10th decimal place will be increased by 1, provided the digit on the 100th place was more than five.
After rounding off the 10th digit, the rest of the numbers can be dropped. It is important to know that the digit in the 10th place remains unchanged if the digit in the 100th place is less than five. In this case, the remainder of the numerals after the 1st decimal point are also omitted.
For example- 5.67
After rounding off – 5.67 becomes 5.7 (as 7 is greater than 5)
What Can you do to round off a numeric value to the nearest hundredths?
Rounding off to the nearest hundredth place is the same as rounding off to estimate the second decimal place. Now, to round off the digit in the 2nd decimal place, one must look at the 1000 place in the given integer value.
If the numeric value of the number coming on the 1000 place is more than five, that one is added to the digit in the 100th place. However, if the digit on the thousandth place is less than five, the number on the 100th place cannot be rounded off. It means the 2nd decimal place remains unchanged.
For example- 4.457
After rounding off- 4.457 becomes 4.46 (as 7 is greater than 5)
It is important to know that estimation is a significant part of arithmetic and useful in everyday life. Estimation allows us to simplify capital sums, distances, time, and an assortment of other physical quantities.
Can you round off decimal numbers with the help of a number line?
It is possible to round off decimal numbers by using a number line. Do you know how to use number lines to estimate decimal values? It is as simple as rounding of other values.
When evaluating certain numeric functions, such as the cost of an object in the store, what can estimate the value and round of decimal numbers for safe utilization.
Decimal numbers are fractional values made up of different parts of the same whole number. The real numbers are given as bold in a number line, and the remaining decimal digits include a decimal point.
Rounding off is a convenient way to estimate an approximate value of the given numeric data. The above information deals with rounding off decimals to the nearest whole number. Apart from this, it is also explained how to round off a given decimal value to its nearest first (tenth) and second place (hundredth). Interestingly, rounding off a certain numeric value helps calculate and estimate for various purposes.