How to Round Numbers to the Nearest Hundred With Simple Tricks
Have you ever scored an 18.5 out of 20, but your teacher says well done, you have scored a good 19 out of 20, and you are left confused about how a teacher can mistakenly increase your score by 0.5? Actually, it is not a mistake, it is a technique called estimation or rounding off a number to simplify it.
Showing Rounding Off of a Number
Rounding off a number means estimating or changing the number to the one it is closest to. Rounding off is a technique used in various subjects like Physics, Chemistry, and Mathematics.
Rounding off implies a number is simplified by changing its worth nearer to the closest number. It may be applied well for any whole number, decimal at different spots of hundreds, tens, tenths, and so on. Rounding off a number is done to maintain the significant figures.
Significant Figures
A significant figure is the number of positional digits in a number that is reliable and necessary to indicate the necessary quantity or meaning.
The number 23.4 has a total of 3 significant figures. According to the rules, every non-zero digit in a number is always significant. 6.21388 has six significant digits (all the numbers counted as significant give useful information). Thus, 82 has two significant digits, and 82.6 has three significant digits.
How to Round off: Rounding off Rules
Rounding Rules for Whole Numbers
To answer the question of how to round off, there are a few simple steps to be always followed. Those are as follows:
Step 1: To obtain a precise end result, carefully pick the last place value.
Step 2: Search for the next smallest place, which is towards the right of the number that is being estimated. For instance, if you want to estimate a digit from a tens place, look for a digit at the one's place.
Step 3: If the digit succeeding the number to be rounded off is under 5, the digit remains unchanged. Any number of digits after that number is converted to zero, and this is called rounding down.
Step 4: If the digit succeeding the number to be rounded off is greater than 5, the digit is increased by 1 this is called rounding up.
Step 5: If the digit succeeding the digit to be rounded off is 5 or 5 followed by 0’s, then the figure to be rounded shall be
incremented by 1 if it is odd, and
unchanged if even. In this case, 0 is considered an even number.
Phenomenon of Rounding Up and Rounding Down a Number
For example, in the above image, 69 is rounding up, and 54 is rounding down by applying the rule discussed in step 5.
Rounding Rules for Decimal Numbers
Step 1: Look for the digit to be rounded and look at its preceding number.
Step 2: If the digits preceding the number to be rounded off are under 5, consider them equal to zero.
Step 3: If the digits preceding the number to be rounded off are greater than or equivalent to 5, then the number is increased by 1.
Rounding Off the Decimals
Rounding off to the Nearest 100
Let's take the example of the number 4850. To round off this number to its nearest hundreds of places and following are the steps:
Step 1: First, identify the digit present at the hundreds place: 8
Step 2: Then, identify the next smallest place in the number: 5
Step 3: As per the rules, if the smallest place digit is greater than or equivalent to 5, round up the digit. Therefore, add +1 to the digit at the hundreds place. 8+1=9. And the other digits become zero.
Answer: So the final number is 4900.
Solved Examples
Q 1. Round off 1647 to the nearest hundreds.
Ans: The answer to the question will be 1700
Step 1: First, identify the digit present at the hundreds place: 6
Step 2: Then, identify the next smallest place in the number: 4
Step 3: As per the rules, if the digits preceding the no. to be rounded off are under 5, then consider them equal to zero. Therefore, the digit at the hundreds place remains the same. And the other digits become zero. So the final number is 1600.
Q 2. What is the nearest number after rounding off the following numbers to the nearest hundreds?
1863
4265
430
Ans: Let's round off the following one by one by using the rules of rounding off to a hundred
A. 1863
Step 1: First, identify the digit present at the hundreds place: 8
Step 2: Then, identify the next smallest place in the number: 6
Step 3: As per the rules, if the smallest place digit is greater than or equivalent to 5, round up the digit. Therefore, add +1 to the digit at the hundreds place. 8+1=9. And the other digits become zero. So the final number is 1900.
B. 4265
Step 1:First, identify the digit present at the hundreds place: 2
Step 2: Then, identify the next smallest place in the number: 6
Step 3: As per the rules, if the smallest place digit is greater than or equivalent to 5, then round up the digit. Therefore, add +1 to the digit at the hundreds place. 2+1=3. And the other digits become zero. So the final number is 4300.
C. 430
Step 1: First, identify the digit present at the hundreds place: 4
Step 2: Then, identify the next smallest place in the number: 3
Step 3: As per the rules, if the digit succeeding the number to be rounded off is under 5, the digit remains unchanged. Any number of digits after that number is converted to zero. So the final number is 400.
Q 3. Round the following numbers to the nearest hundred.
3,00,678
13,05,889
Ans:
1. 3,00,678 is the Given Number.
We can determine that the number's digit in the tens position is 7, which is greater than five. Therefore, add a 1 to the hundreds place, and add zeros in the units and tens of the number. Thus, 3,00,700 is the result of rounding 3,00,678 to the nearest hundred.
2. 13,05,889 is the Given Number.
We round to the nearest multiple of the hundred places bigger than the integer when the digit in the tens place is 8, which we see. 13, 05, 889 is closer to 13, 05, 900 than 13, 05, 800.
Practice Questions
Q 1. Round off 5672.8 to the nearest 100.
Ans: 5700
Q 2. Round of 5681 to the nearest hundreds.
Ans: 5700
Q 3. What is the nearest number after rounding off the following to the nearest 100.
9832
441
Ans: a) 10000 b) 400
Summary
Keeping a number's value close to its original value while simplifying it is known as rounding. The outcome of rounding off is less precise but simpler, particularly when doing mathematical procedures. Similar to this, rounding a number to the closest hundred entails placing zeros in the units and tens and increasing or decreasing the remainder by one. In the areas of this website, students can find examples of solved problems, definitions, and round-off guidelines.
FAQs on Rounding Off to the Nearest 100 Made Easy
1. What is the rule for rounding off numbers to the nearest 100?
To round a number to the nearest 100, you must first look at the digit in the tens place. This digit tells you whether to round up or down.
- If the tens digit is 4 or less (0, 1, 2, 3, 4), you round down. The hundreds digit stays the same, and the tens and ones digits become zero.
- If the tens digit is 5 or more (5, 6, 7, 8, 9), you round up. The hundreds digit is increased by one, and the tens and ones digits become zero.
2. How do you round 473 to the nearest 100? Give an example.
To round the number 473 to the nearest 100, we follow the rule by examining the digit in the tens place, which is 7. Since 7 is greater than 5, we must round up. This involves increasing the hundreds digit (4) by one to make it 5, and then changing the tens and ones digits to zero. Therefore, 473 rounded to the nearest 100 is 500.
3. Can you round a 4-digit number like 3789 to the nearest 100?
Yes, the rounding process works the same way for larger numbers. To round 3789 to the nearest 100, we focus only on the tens digit, which is 8. As 8 is greater than 5, we round up. The hundreds digit (7) increases to 8, while the tens and ones digits become zero. The thousands digit (3) is not affected. So, 3789 rounded to the nearest 100 is 3800.
4. Why is the digit in the tens place important when rounding to the nearest 100?
The tens place digit is crucial because it determines whether a number is closer to the preceding hundred or the next hundred. Think of 100 as a whole unit; the halfway point is 50. The tens digit shows us where the number falls relative to this halfway mark.
- If the tens digit is 4 or less, the value of the last two digits is 49 or less, which is closer to 0 than to 100. So, we round down.
- If the tens digit is 5 or more, the value is 50 or more, which is halfway to or closer to the next 100. So, we round up.
5. What happens if the tens digit is exactly 5 when rounding to the nearest 100, for example, with the number 250?
When the tens digit is exactly 5, the number is precisely in the middle of two hundreds (e.g., 250 is halfway between 200 and 300). In mathematics, the standard rule to ensure consistency is to always round up in this case. Therefore, 250 rounded to the nearest 100 becomes 300. This convention prevents ambiguity in calculations.
6. In what real-life situations would you use rounding off to the nearest 100?
Rounding to the nearest 100 is a practical skill used for making quick estimations in daily life, especially with larger numbers. For example:
- Budgeting: If monthly bills are ₹1280 and ₹830, you can round them to ₹1300 and ₹800 to quickly estimate your expenses as ₹2100.
- Shopping: Estimating the total cost of groceries. An item costing ₹295 is about ₹300.
- Measurements: When discussing large distances, one might say a city is "about 400 km away" instead of the exact 412 km.
7. How is rounding to the nearest 100 different from rounding to the nearest 10?
The key difference is the place value you check and the level of precision in the result.
- When rounding to the nearest 10, you inspect the ones digit. The result is a multiple of 10. For example, the number 647 becomes 650.
- When rounding to the nearest 100, you inspect the tens digit. The result is a multiple of 100. The same number, 647, becomes 600.
8. How can rounding to the nearest 100 help in estimating the sum of two numbers, like 723 and 586?
Rounding helps simplify complex calculations into mental maths. To estimate the sum of 723 and 586, you round each number first:
- Round 723: The tens digit is 2 (less than 5), so it rounds down to 700.
- Round 586: The tens digit is 8 (greater than 5), so it rounds up to 600.
- Add the estimates: 700 + 600 = 1300.
This gives you a very close approximation to the exact answer (1309) much more quickly.
