What are Numbers ?
A number is an arithmetic value that is used to represent a quantity and to perform calculations. It is an arranged set of digits. A symbol such as “5” that represents a number is known as a numeral. Numbers are a significant part of our everyday lives. Without numbers, we will not be able to count, check the date or time, or even exchange money.
What is a Number line?
A number line is a visual representation of numbers on a straight line, drawn horizontally or vertically. By writing numbers down on a number line, we can compare them and perform basic arithmetic operations. The three parts of a number line are the negative side, the zero, and the positive side, as shown below.
What is Place Value?
The value of each digit in a number is known as its place value. In other words, every digit in a number has a different value depending on its position. A number may have two digits that are similar but have different values, which is determined by the digit’s position in the number.
A number may comprise the same two digits, but the value of the digits will be different. For instance, in the number 622, 2 in the ten’s place represents 20, and the 2 in the one’s place represents 2. Hence, although the digits are the same, the value they represent differs.
For example, the number 469 can be represented as:
Here, 4 represents 4 hundreds, i.e., 400, 6 represents 6 tens, i.e., 60, and 9 represents 9 ones, i.e., 9.
Rounding Off a Number Using a Number Line:
To round a number to the nearest ten or hundred, replace the number with its nearest multiple of ten or hundred. Round to the greater number when a number is exactly halfway between two multiples of ten or hundred. If the number to be rounded lies to the left of the halfway number, then it is rounded to the multiple to the left of the halfway number. Similarly, if the number is to the right of the halfway number, then the number is rounded to the multiple to the right of the halfway number.
Rounding Off a Number Using Place Value:
To round off a number using place value:
- Note the digit at the place to which you are rounding.
- Take a look at the digit on its right. If the number is less than 5, the digit in the rounding place remains the same. If it’s 5 or more, the digit in the place you’re rounding goes up by one.
- For all the digits to the right of the place you’re rounding, write zeros.
Solved Rounding Off Number Examples:
Examples 1:
Round 52 to the nearest ten.
Solution:
52 lies between 50 and 60.
52 is closer to 50 than it is to 60.
So, 52 rounded to the nearest ten is 50.
Example 2:
Round 865 to the nearest hundred.
Solution:
Plot 865 on a number line:
865 is closer to 900 than it is to 800.
So, 865 rounded to the nearest hundred is 900.
Example 3:
Round 435 to the nearest hundred and the nearest ten.
Solution:
435 rounded to the nearest hundred is 400.
435 rounded to the nearest ten is 440.
Example 4:
The cost of a laptop is $1599. Find the nearest rounded cost to thousands.
Solution:
To round 1599 to the nearest thousand, the rounding digit at the place of thousand is 1. The digit to the right of the rounding digit is 5. This indicates that we have to increase the thousands-place digit by 1 and replace the other digits with zeros.
We can conclude that $1599 rounded to the nearest thousand is $2000.
Example 5:
Robert’s house is at a distance of 2628 feet from his school. Find the distance to the nearest hundred.
Solution:
So, we can conclude that 2,628 feet rounded to the nearest hundred is 2,600 feet.
To round 2,628 to the nearest hundred, the rounding digit at the place of hundred is 6. The digit to the right of the rounding digit is 2, which is smaller than 5. So, we have to replace all the digits to the right of the hundreds digit with zeros.
So, we can conclude that 2,628 feet rounded to the nearest hundred is 2,600 feet.
Rounding off a number shows us how to convert it to a simpler value that is close to its original value. Rounding numbers makes calculations easier and converts figures into easy-to-remember approximate values.
For example, if a town’s population is 692,769, it can be rounded to 700,000. An approximate figure of 700,000 is easier to remember than the actual figure.
The approximation of numbers gives us a quick estimate of the result of a complicated calculation.
If the number being rounded off is followed by the digits from 5 to 9, the round-up place is increased by one. This is referred to as rounding up a number.