Quick Examples: Rounding Decimals to the Nearest Hundredth
What is the Concept Behind Rounding-off?
The concept of rounding-off was developed to get the approximate value of numbers in decimal because any number like 23.1345 would look odd but when we can make it simpler to 23.13 i.e., to the nearest hundredth value. Thus, rounding off makes the long decimal numbers easier to remember.
We stated that rounding-off is similar to approximation and we represent it by a symbol ≈, which is a short way to display the round-off of any number because the math works more on symbols than prolonged statements.
Now, let us get through the process of finding the round-off of a number to the nearest hundredth with solved examples.
Process to Round-off to the Nearest Hundredth
In Maths, the decimal numbers are the numbers that rely on the powers of 10, which means when we move from left to right, the place value of the number gets divided by 10.
Hence, the place value system is the best method to determine the tenths, hundredths, thousandths, and so on of the digits of any given number.
Here, tenth means 1/10, hundredth means 1/100, thousandth means 1/1000, and so on.
What is the Hundredth of a Number?
The image you can see below clearly shows the place value of a decimal number.
Representation of the hundredth place of a decimal number?
So, the digits to the left are 5 and 1, where 1 is at the one’s place and 5 is at the tens place, which means from right to left, the place value increases. Whereas going from left to right after the decimal point, we notice that the place value of ‘0’ is at tenths place or1/10, 4 at hundredths place or 4/100, 8 is at thousandths place or 8/1000, and so on.
While rounding the number to its nearest hundredth place, we must follow the given steps:
Let us assume a decimal number: 3.1736
Now, we have to round off the number 3. 1736 to its nearest hundredth value.
Step 1: Firstly, we need to recognise the hundredth digit. (Here, 7 is the digit in the hundredth position or it has the hundredth place value)
Step 2: Now, we proceed with the digit that is just next to the hundredth digit. (Here, 3 is the digit, which is just after the hundredth digit)
Step 3: Now, we need to check whether the digit next to the hundredth place is greater than or equal to 5, round up the hundredth digit, or else round down the hundredth digit. (Here, we notice that 3 is less than 5, so we round down).
Step 4: Since the digit after the hundredth place was lesser than 5 so the digit at the hundredth place remains the same as 6, as 2 is less than 5.
Hence, the number 3.1736 rounds off to its nearest hundredth as 3.17.
Examples of Rounding off to the Nearest Hundredth
6. 1234
Here, 2 is the digit at the hundredth place and the digit just after it is ‘3’ which is lesser than 5, so the 6.1234 rounds off to 6.12
5.1289
Here, 2 is at the hundredth place and 8 is at the thousandth place which is greater than 5, so here we have a new case when 8 > 5 and ‘2’ at the hundredth place changes to ‘3’. Hence, the round-off to the nearest hundredth becomes 5.13 for 5.1289.
A Fact to Remember:
Approximately equal to sign is often used to indicate rounding of exact numbers, e.g., 9.98 ≈ 10. This sign was introduced by Alfred George Greenhill in 1892.
So, this was all about the round-off concept. The above context explains to us that if the digit at the thousandth place is lesser than 5 then we just take two places after the decimal as such (we did in an example 3.1736). However, when the same digit is greater than 5, we increase the value of the digit at the hundredths place by 1, as we did in the example of 5.1289.
FAQs on How to Round Off Numbers to the Nearest Hundredth
1. What does it mean to round off a number to the nearest hundredth?
To round off a number to the nearest hundredth means to simplify it to a number with only two decimal places. The hundredths place is the second digit after the decimal point. This process makes the number easier to work with while keeping its value very close to the original.
2. What is the rule for rounding a decimal to the nearest hundredth?
To round a decimal to the nearest hundredth, follow these steps as per the CBSE/NCERT 2025-26 syllabus:
Identify the digit in the hundredths place (the second digit after the decimal).
Look at the digit immediately to its right, which is in the thousandths place.
If the thousandths digit is 5 or more (5, 6, 7, 8, or 9), you round up the hundredths digit by one.
If the thousandths digit is 4 or less (0, 1, 2, 3, or 4), you keep the hundredths digit the same.
Finally, drop all digits to the right of the hundredths place.
3. Can you give an example of rounding up to the nearest hundredth?
Certainly. Let's round the number 7.268 to the nearest hundredth. The digit in the hundredths place is 6. The digit to its right (in the thousandths place) is 8. Since 8 is 5 or more, we round up the hundredths digit (6) to 7. Therefore, 7.268 rounded to the nearest hundredth is 7.27.
4. When does a number's value remain the same after rounding to the nearest hundredth?
A number's hundredths digit stays the same when the digit in the thousandths place is 4 or less. For example, to round 45.823, we look at the thousandths digit, which is 3. Since 3 is less than 5, we keep the hundredths digit (2) as it is and drop the 3. The rounded number is 45.82.
5. Where do we use rounding to the nearest hundredth in real life?
Rounding to the nearest hundredth is very common in real-life applications, especially those involving money. Since currency is often divided into 100 parts (e.g., 100 paise in a rupee), prices and financial calculations are expressed to two decimal places. It is also used in:
- Scientific Measurements: Recording weight, length, or volume with precision (e.g., 2.45 metres).
- Sports: Timing events like races, where results are often measured to the hundredth of a second.
- Percentages: Calculating precise percentages, such as interest rates or statistical data.
6. How does the thousandths digit actually determine the rounding for the hundredths place?
The thousandths digit acts as a decision-maker because it tells us which hundredth the number is closer to. Think of a number line. If the thousandths digit is 5 or more, it signifies that the number is at least halfway towards the next higher hundredth, so we round up to that closer value. If the thousandths digit is 4 or less, the number is closer to the current hundredth, so we round down (by keeping the hundredth digit the same).
7. What is the difference between rounding to the nearest hundredth and the nearest tenth?
The key difference is the level of precision required:
Rounding to the nearest tenth simplifies a number to have only one digit after the decimal. You use the hundredths digit to make the decision. For example, 5.86 rounded to the nearest tenth is 5.9.
Rounding to the nearest hundredth is more precise, simplifying a number to have two digits after the decimal. You use the thousandths digit to decide. For example, 5.864 rounded to the nearest hundredth is 5.86.
8. What is a common mistake to avoid when rounding decimals to the nearest hundredth?
A very common mistake is looking at the wrong digit to make the rounding decision. Students sometimes look at the digit in the tenths place or another digit instead of the thousandths place. For example, when rounding 13.756, the correct approach is to look at the 6 (thousandths) to round the 5 (hundredths) up to 6, making the answer 13.76. Always focus only on the digit immediately to the right of the place you are rounding to.
9. If a number is exactly halfway, like 8.425, how do you round it to the nearest hundredth?
In mathematics, the standard convention is to round up when a number's deciding digit is exactly 5. For the number 8.425, the digit in the thousandths place is 5. Following the rule '5 or more, round up', the hundredths digit (2) is increased by one. Therefore, 8.425 is rounded to 8.43. This consistent rule prevents ambiguity in calculations.
