Step-by-Step Guide: How to Round Numbers Correctly
Rounding simply refers to making a number simpler while keeping its value nearest to what it was. The outcome however will be less exact, but much easier to use. Example: 92 rounded to the nearest ten are 90 since 92 is closer to 90 than to 100. When rounding a number, you first need to see: what are you rounding it to? We can round the numbers to the nearest ten, the nearest hundred, the nearest thousand, and so on.
Rounding Decimals
Let us see how we perform rounding decimals.
Say we want to round the number 728.363. Typically based upon which place value we'll round to, the final outcome will differ. Rounding 728.363:
Rounding to the nearest hundred, we get 700.
Rounding to the nearest ten, we get 730.
Rounding to the nearest one, we get 728.
Rounding to the nearest tenth, we get 728.4.
Tips for Rounding Decimals
In order to avoid confusion or make errors while solving rounding numbers or rounding long decimals, just consider only the number in the place you are rounding to and also the number that follows it. For example, to round 4.273891401 to the nearest hundredth (100th), just look at the number from the left in the hundredths place—7—and the number that follows it—2. Then you can easily round it to 4.27.
How to do Rounding of Fractions?
Rounding fractions works just in a similar manner as rounding whole numbers. The only difference is that rather than rounding to 10s (tens), (100s) hundreds, thousands (1000s), and so on, we just round to 10th (tenths), 100th (hundredths), 1000th (thousandths), and so on. Let’s consider some examples to get a knowhow of the concept better:
6.7199 rounded to the nearest tenth (10th) is 6.7.
2.0731 rounded to the nearest hundredth (100th) is 2.07.
4.8693 rounded to the nearest thousandth (1000th) is 4.869.
How to do Rounding and Sums?
Rounding can certainly make sums easy. For instance, at a merchant shop you might choose articles with the following prices:
Rs. 3.35
Rs. 0.77
Rs. 1.68
If you wanted to know how much they would cost, you could add up the prices using a calculator, or try to just add them in your head. Or you could simply estimate by rounding off to the nearest rupees, like this:
Rs. 3.00
Rs. 1.00
Rs. 2.00
By rounding off, we could easily find out that we would require about Rs. 6.00 to pay for the items purchased. If you see, this is quite close to the exact number of Rs. 5.8.
Rounding a Number to The Nearest Ten
Round to the Nearest Ten: 799.
Determine the tens digit: the 1st 9 in 799.
Determine the next smallest place value: the 2nd 9 in 799.
Is that digit ≥ five? Thus, round up.
The tens digit increases by one. Because 9+1=10, you would require to carry the 1 and add it to the digit in the 100s place. Each digit then after becomes a zero.
799 rounded to the nearest ten is 800.
Rounding a Number to The Nearest Hundred
Let’s take a digit 4350.
Round to the Nearest Hundred: 4350
Determine the hundreds digit: the 3 in 4350
Determine the next smallest place value: the 5 in 4350
Is that digit ≥ five? : Yes, therefore round up.
Increase the hundreds digit by one, so 3 becomes 4. Every digit after becomes a zero.
4350 rounded to the nearest hundred is 4450.
Did You Know?
A few statisticians prefer to round 5 to the nearest even number.
As a result of rounding 5 to the nearest even number, about half of the time five (5) will be rounded up, and about half of the time, it will be rounded down.
In this way, 38.5 rounded to the nearest even number would be 38—it would be rounded down. And, 38.5 rounded to the nearest even number would be 39—it would be rounded up.
Conclusion
In order to learn how to round a number to its nearest multiple, you can check the online round to nearest multiple calculators. The calculator is a useful tool to round to multiples of whole numbers or decimals.
How to Prepare Notes on Rounding Numbers?
All students must go through Rounding
This page has explained everything in detail
Students can read up the matter here and then highlight all the important areas
They can follow the sequence that’s here and then understand whatever has been explained
They must not copy everything from the page but write them down in their own words
They can use drawings and other forms of illustrations to better understand the topic
They can then revise from the same before a test
Does Vedantu have any Material on Rounding Numbers?
Yes, Vedantu has ample study material on Rounding numbers. All students can read from Rounding and understand the topics better. They can go through this page as it has all the information that they need. This material can be accessed in the form of a PDF offline even when students do not have access to the internet.
FAQs on Rounding Numbers Made Simple
1. What does 'rounding numbers' mean in Maths?
In Maths, rounding numbers means simplifying a number to its nearest place value, such as the nearest ten, hundred, or thousand, to make it easier to work with. The resulting number is an approximation of the original value. For example, if you have 78 students, you might say there are approximately 80 students, which is rounding 78 to the nearest ten.
2. What are the basic rules for rounding numbers?
The basic rules for rounding numbers are based on the digit to the right of the place value you are rounding to:
- Identify the rounding digit: This is the digit in the place value you want to round to (e.g., the tens digit).
- Look at the digit to its right: This is the deciding digit.
- Rule 1 (Rounding Up): If the deciding digit is 5, 6, 7, 8, or 9, you increase the rounding digit by one. All digits to the right of the rounding digit become zeros.
- Rule 2 (Rounding Down): If the deciding digit is 0, 1, 2, 3, or 4, you keep the rounding digit the same. All digits to the right also become zeros.
3. How do you round a number to the nearest ten with an example?
To round a number to the nearest ten, you look at the ones digit. Let's take the number 47.
- The digit in the tens place is 4 (the rounding digit).
- The digit in the ones place is 7 (the deciding digit).
- Since 7 is 5 or more, we round up the tens digit.
- The 4 becomes a 5, and the ones digit becomes 0.
4. How is rounding to the nearest hundred different from rounding to the nearest ten?
The key difference is the place value you focus on. When rounding to the nearest ten, you look at the ones digit. When rounding to the nearest hundred, you look at the tens digit. For example, consider the number 238:
- To the nearest ten: We look at the 8 (ones digit). Since it's 5 or more, we round up the 3. So, 238 becomes 240.
- To the nearest hundred: We look at the 3 (tens digit). Since it's less than 5, we round down, keeping the 2. So, 238 becomes 200.
5. What is the importance of rounding numbers in real life?
Rounding numbers is very important in daily life for making quick estimations and simplifying complex numbers. Real-life examples include:
- Shopping: Estimating the total cost of groceries. If items cost ₹48, ₹99, and ₹52, you can round them to ₹50, ₹100, and ₹50 to quickly estimate the total is around ₹200.
- Reporting Large Numbers: News reports often use rounded numbers for populations or budgets (e.g., 'a city of 3 million people' instead of 2,987,456).
- Time Management: Saying 'I'll be there in about 20 minutes' is an example of rounding time for convenience.
6. How are decimal numbers rounded?
Rounding decimals follows the same principle as whole numbers, but you focus on the place values to the right of the decimal point (tenths, hundredths, etc.). For example, to round 8.76 to the nearest tenth:
- The digit in the tenths place is 7.
- The digit to its right (in the hundredths place) is 6.
- Since 6 is 5 or more, we round up the tenths digit (7).
- The 7 becomes an 8.
7. Why is a number ending in 5, like 45, always rounded up?
A number ending in 5 is exactly in the middle between the two tens (e.g., 45 is exactly halfway between 40 and 50). To avoid confusion and ensure consistency, mathematicians have established a standard rule or convention to always round the half-way point up to the next higher number. This ensures that everyone gets the same result when rounding the same number.
8. What is the difference between rounding and estimation?
While related, rounding and estimation are different. Rounding is a specific mathematical method to find an approximate number based on clear rules. For example, rounding 27 to the nearest ten is always 30. Estimation is a broader term for finding a value that is close to the correct answer. You can estimate an answer using rounding, but you can also use other methods like clustering or front-end estimation. In short, rounding is one of the tools you can use to make an estimate.
9. Can rounding numbers ever lead to an incorrect answer?
Yes, rounding gives an approximate value, not an exact one. While it is excellent for quick calculations and estimations, it can lead to significant errors in situations that require high precision. For example, if you round every item in a large calculation, the final answer could be far from the true value. Therefore, it's not suitable for precise tasks like engineering calculations, scientific experiments, or final financial reports, which require exact figures.
