What are Rounding Decimals?
In mathematics, decimal rounding is a method used to measure or locate estimated values and to restrict the sum of decimal positions. Rounding off decimals is an occurrence that we experience most of the time in our everyday lives.
Some of the physical uses of rounding decimals are the calculation of the expense of the products, the distance between the two lines, the length of the objects, and the weight of the goods. These amounts are calculated by rounding off their values to a defined precision.
What are Decimals?
The Decimal Number System is a common system for denoting integer and non-integer quantities. It is an extension of the non-integer numbers of the Hindu-Arab numeral system. The method of denoting numbers in the metric system is also referred to as decimal notation. Decimal numeral usually refers to the notation of a number in the decimal numeral system. Decimals may also be defined by a decimal separator. Decimal can also refer directly to the digits after the decimal separator, such as '3.14 is the approximation of the two decimal digits'.
Why is Estimation Important?
What Is Rounding? Rounding off means finding the estimation or approximation. Estimation (or estimation) is the method of finding an estimate or approximation and is a value that may be used for any reason even though the input data may be imperfect, unreliable, or unpredictable. However, the value is functional since it is extracted from the latest available knowledge. Usually, the calculation requires "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter" The sample contains information that can be predicted through different formal or informal methods to define the spectrum most likely to represent the missing information. A calculation that turned out to be inaccurate will be an overestimation if the estimate approaches the actual result, and an underestimation if the estimate falls short of the actual result. In mathematics, approximation defines the method of finding predictions in the form of upper or lower limits for a quantity that cannot easily be precisely measured, and approximation theory deals with finding simpler functions that are similar to any complicated function and that can provide useful estimates.
In statistics, the estimator is the formal name of the law under which the value is derived from the data, and the estimation principle deals with the discovery of values of good properties.
How to Round Off Decimal Numbers?
Rounding off is an arithmetic method used to locate an estimate of a particular number. Decimal numbers are rounded off to a designated decimal point to make them easier to grasp and handle, instead of providing a long series of decimal places.
Following are the Rules For Rounding Decimals:
Round off the decimal number to the closest whole number.
Rounding to the nearest tenths or, in other words, to one decimal place.
Rounding to the nearest hundredths, which is the same as rounding to two decimal points.
Rounding Off Decimal Numbers to the Nearest Whole Number
On Rounding off Decimals to the nearest whole number, the tenth digit is tested if it is above or below 5. If the tenth is equal to or greater than 5, the number is rounded up, and if the tenth digit is less than 5, the number is rounded down. Rounding up a number where the tenth digit is higher than or equal to 5 is essentially applying 1 unit to the one-digit or the first digit to the left of the decimal point. You write the remaining numbers after you lower all the numbers to the right after the decimal point.
Rounding Off a Decimal Number to the Nearest Tenths
Rounding a number to the nearest tenths is the same as rounding a number to 1 decimal place. In this case, the digit is identified in the 100th place. If the digit in the 100th place is greater than or equal to 5, the 10th digit shall be increased by one unit. The rest of the numbers are dropped after the tenth digit. If the digit in the 100th place is equal to or less than 4, the digit in the 10th place shall remain unchanged. Likewise, the rest of the numbers after the tenth digit are dropped.
Rounding Off a Number to the Nearest Hundredths
Rounding to the nearest hundredths is the same as rounding to two decimal places. To round off a number to two decimal places, look at the digit in a thousandth place. If the digit in the thousandths place is greater than or equal to 5, the hundredths digit shall be increased by one unit. And if the digit in the thousandths place is equal to or less than 4, the digit in the hundredths places will remain unchanged. Estimating is an integral aspect of mathematics and a very valuable method for daily life. Get used to estimating sums of capital, periods, distances, and many other physical quantities.
How to Rounding Off Whole Numbers?
Find the place value you want (the "rounding digit") and look at the digit to the right.
If the digit is less than 5, do not change the "rounding digit" but change all digits to the right of the "rounding digit" to 0.
If the digit is greater than or equal to 5, add one to the rounding digit and change all digits to the right of the rounding digit to 0.
Rounding Decimal Numbers Using Number Line
How do we Round off Decimals Using Number Lines? Rounding Decimal Numbers is a safe method to use when calculating sums, for example, the expense of the merchandise in the shop. Decimal numbers are parts of whole numbers, equivalent to fractions. The bold numbers in the number line below are whole numbers. The other digits - they have a decimal point in them - are decimal numbers.
Solved Examples
1. Round off each of the following to the nearest whole number: 8.71.
Ans: In arithmetic, whole numbers are the simple numbers 0, 1, 2, 3, 4, 5, 6, ... and so on. Whole numbers include natural numbers starting from 1 onwards. Whole numbers contain positive integers and 0. Therefore, on Rounding Off Decimals the nearest whole number to 8.71 is 9.
2. Round 74.862 to the closest tenths.
Ans: The tenth place digit is 8. The digit on the right of 8 is 6. We've rounded up since 6 > 5.
74.862 is 74.9 rounded to the nearest tenths.
Fun Facts
The decimal 'dec' means ten, which refers to the fact that each position in a decimal number is 10 times more than the next position along with it.
Some decimal expansions carry on forever: for example, 1/3 = 0.333... where the '...' means that the 3s never stops.
For the decimal point, various countries and languages use different notations. For eg, in Taiwan and Singapore, the point is put in the middle of the line, so 23·89 instead of 23.89. Instead, a comma is seen in many European countries: 23,89.
FAQs on Rounding Decimals
1. What are the basic rules for rounding decimals?
To round a decimal, you first identify the digit in the place value you are rounding to (the 'rounding digit'). Then, look at the digit immediately to its right. The two main rules are:
- If the digit to the right is 4 or less, you keep the rounding digit the same and drop all the digits to its right. This is called rounding down.
- If the digit to the right is 5 or more, you add one to the rounding digit and drop all the digits to its right. This is called rounding up.
2. How do you round a decimal to the nearest whole number?
To round a decimal to the nearest whole number, you need to look at the digit in the tenths place (the first digit after the decimal point). For example, to round 15.72, the tenths digit is 7. Since 7 is 5 or more, you round up the whole number part. So, 15.72 rounds to 16. If the number was 15.32, the tenths digit is 3 (less than 5), so you would round down and the answer would be 15.
3. What is the process for rounding a decimal to the nearest tenth?
When rounding to the nearest tenth, you focus on the digit in the hundredths place (the second digit after the decimal point). For example, to round 8.461 to the nearest tenth, the hundredths digit is 6. Since 6 is greater than 5, you round up the tenths digit (4 becomes 5). The answer is 8.5.
4. How do you round a number like 64.9963 to two decimal places (the nearest hundredth)?
This is a special case that involves carrying over. To round 64.9963 to the nearest hundredth, we look at the thousandths digit, which is 6. Since 6 is greater than 5, we must round up the hundredths digit (the second 9).
- Adding 1 to the hundredths digit (9) makes it 10. We write down 0 and carry over 1 to the tenths place.
- Adding the carried-over 1 to the tenths digit (9) also makes it 10. We write down 0 and carry over 1 to the units place.
- Adding the carried-over 1 to the units digit (4) makes it 5.
Therefore, 64.9963 rounded to two decimal places is 65.00.
5. What is the special rule for rounding a number when the deciding digit is exactly 5?
When the digit you are checking is exactly 5, the standard rule is to round up. For example, if you need to round 2.35 to the nearest tenth, you look at the 5. According to the rule, you round up the tenths digit (3 becomes 4). The final answer is 2.4. Similarly, 0.5 rounded to the nearest whole number is 1.
6. Why is rounding decimals important in real life?
Rounding decimals is a very practical skill used in many everyday situations to make numbers simpler and easier to work with. For example:
- Shopping: When you calculate the price of items, you round to two decimal places for rupees and paise (e.g., ₹25.75).
- Measurements: When measuring height, weight, or distance, we often round the numbers to a convenient value. A carpenter might round a measurement of 15.2 cm to 15 cm.
- Data and Statistics: When presenting data like population or survey results, large numbers are often rounded for easier understanding.
7. What is the difference between rounding and truncating decimals?
Rounding and truncating are two different ways to simplify a decimal, but they can give different results. Truncating means to simply cut off the decimal at a certain point without changing the last digit. Rounding involves checking the next digit to decide whether to keep the last digit the same or increase it. For example, with the number 7.89:
- Truncating to one decimal place would be 7.8.
- Rounding to one decimal place would be 7.9 (because the hundredths digit, 9, is 5 or more).
8. Does rounding a decimal always make the number bigger?
No, this is a common misconception. Rounding a decimal does not always make it bigger. It depends on the digit being dropped. If you are rounding up (because the digit is 5 or more), the value increases. However, if you are rounding down (because the digit is 4 or less), the value of the number actually decreases. For example, rounding 3.14 to the nearest tenth gives 3.1, which is smaller.
