Use of Place Value and Number Line to Round Numbers
Rounding off a number is a way of representing it in a simpler form by altering its digits. Rounding a number makes typical calculations easier. However, the final answer is always an estimated value of the exact answer.
In mathematics or science, physical quantities like distance, length, weight and so on are rounded off to make the calculations simpler. Rounding gives an answer close to the exact answer in any problem, which helps in reducing the time of calculation largely.
Depending on its value, a number can be rounded off to a multiple of 10 or 100 or 1000 and so on, whichever is closest to the actual number. We can round a number by two methods:
1. Using a number line
2. Using place value
Rounding off a Number Using a Number Line
A number can be rounded off using a number line using the following steps:
Step 1: Draw a number line with a range of whole numbers as per the given number.
The numbers on the number line should be of the place value to which the given number is to be rounded off.
Step 2: Mark the halfway number on the line. The halfway number is the number corresponding to the midpoint of the line.
Step 3: Now mark the given number on the line.
Step 4: See whether the number is on the left or right of the halfway mark.
If the number lies towards the left of the halfway number then, the next number on the left side is the rounded number.
Else, if the number falls towards the right of the halfway number then, the next number on the right is the rounded number.
For example: Round off 4309 to the nearest thousands.
Step 1- Draw a number line around 4309 that contains numbers of thousands place value i.e. from 4000 to 5000.
Step 2- Mark the halfway number 4500 on the line.
Step 3- Mark the given number, 4309 on the line.
Step 4- Now look whether it is to the right or left of the halfway number.
The number 4309 is on the left of the halfway mark, 4500 i.e. it is closer to 4000 than 5000.
Therefore, 4309 rounded off to the nearest thousand is 4000.
Let’s take another example, round the number 580 to the nearest hundred.
Applying the same steps as in previous example we get,
It is observed that 585 lies to the right of the halfway number, 550 i.e. 585 is closer to 600.
Therefore, 585 rounded off to the nearest hundred is 600.
Rounding a Number Using Place Value
A number can be rounded to the nearest tens, hundreds or thousands using the concept of place value without using a number line.
For this we should know the rounding digit. A rounding digit is the number at the place value about which we round up, or round down, any number.
For example, if we use place value to round 485,920 to the nearest ten thousands. Then the digit at the “ten thousands” place is 8. So, the rounding digit is 8.
Case 1: Digit to the right of rounding digit > 5 or = 5
If the digit to the right of the rounding digit is equal to or greater than 5, then the rounding digit increases by one and all the remaining digits to its right are reduced to 0.
This is called rounding up of a number.
For example, if we use place value to round 465,918 to the nearest ten thousands.
Then the digit at the ten thousands place is 6, so the rounding digit is 6.
The digit to the right of the rounding digit is 5. So, increase the rounding digit by 1 and make remaining rightward digits 0.
So, 465,918 rounded to the nearest ten thousand is 470000.
Case 2: Digit to the right of rounding digit > or = 5
If the digit to the right of the rounding digit is less than 5, then the rounding digit decreases by one and all remaining digits to its right are reduced to 0.
This is called rounding down a number.
For example, if we want to round 554,256 to the nearest ten thousand then,
The digit at the place of ten thousand is 5, so the rounding digit is 5.
The digit to the right of the rounding digit is 5. So, keep the rounding digit the same and make remaining rightward digits 0.
So, 554,256 rounded to the nearest ten thousand is 550,000.
Solved Examples
Example 1:
Round the number 593,259 to the nearest thousands using a number line.
Solution:
To round off a number 593,259 to the nearest thousand we follow the following steps,
First draw a number line around 593,259 containing numbers of thousands place values.
Then mark the halfway number i.e. 593,500.
At last, mark the number 593,259 on the number line and check whether it is to the left or right of the halfway mark.
The number is on the left side of the halfway number.
Therefore, 593,259, rounded off to the nearest thousand is 593,000.
Example 2:
Round the number 8559 to the nearest hundreds using a number line.
Solution:
To round off 8559 to the nearest hundreds, first draw a number line around 8559 containing numbers of hundreds place values.
Then mark the halfway number, i.e. 8550. Then mark the number 8559 on the number line.
Check whether it is to the left or the right of the halfway mark.
Therefore, 8559 rounded off the nearest hundred is 8600.
Example 3:
The price of a laptop is $1599. Find the nearest rounded price to the thousands.
Solution:
To round 1599 to the nearest thousands, the rounding digit at the place of thousand is 1.
The digit right of the rounding digit is 5. So, increase the thousand-place digit by 1 and change the digits occurring on the right of the number to 0.
So, we can conclude that $1599 rounded to the nearest thousand is $2000.
Example 4:
Robert’s house is at a distance of 2628 feet from his school. What is the distance to the nearest hundred?
Solution:
To round 2,628 to the nearest hundred, the rounding digit at the place of hundred is 6.
The digit right of the rounding digit is 2, which is smaller than 5. So, we replace all the digits on the right of 6 with 0.
So, we can conclude that 2628 feet rounded to the nearest hundred is 2600 feet.
If the digit in a number that is being rounded off is followed by digits between 0 to 4 then we convert them into zero. This is called rounding down the number.
Rounding a number gives an approximate value of the number using which we can quickly estimate the answer to a complex calculation.