The Different Forms of Representing Numbers
There are different ways of writing a number. We can represent a number in three different forms:
Representation deals with the method that allows us to express a number to someone else, and the number should be exactly understandable to others as stated.
In our daily life, if someone says the price of a toy is twenty-five dollars, it means he said the number in word form, and this way of expressing a number could be understood. Again, if a price tag on a shirt says ‘$15’, it is said to be in the standard form which is easily understandable.
The Standard Form
If we write a number in digits, separating the groups by commas, the number is said to be in the standard form. We often use the standard form to write the numbers in mathematics. It is also the easiest way of expressing the number. So, it is the most common or obvious way of expressing numbers.
For example,
789,456
4,555
233
789,450, and so on.
The Word Form
If one writes or represents a standard number in words, the form is called the word form. This is the same as when we tell a number to others.
For example, 399 is stated as three hundred ninety-nine.
586,256 in the word form is five hundred eighty-six thousand, two hundred fifty-six.
The Expanded Form
If the number is written as the summation of the place value of each digit, the number is said to be in the expanded form.
For example,
356 in the expanded form is 300 + 50 + 6.
Here, each digit is separated according to its place value. Then the ‘addition’ symbol is mentioned between them. This representation helps us analyze a number easily.
Example: If we take the number 842,062 and make a place value chart as,
This number can be written in three forms as,
The standard form: 842,062.
The word form: Eight hundred forty-two thousand, sixty-two.
The expanded form: 800000 + 40000 + 2000 + 60 + 2.
Solved Examples on Number Representation
Example 1: Write the number in three different forms.
8563
Solution:
The standard form: 8,563.
The word form: Eight thousand, five hundred sixty-three.
The expanded form: 8,000 + 500 + 60 + 3.
Example 2: Write the number in the standard and expanded forms:
Eighty-six thousand, seven hundred and three.
Solution:
The word form is eighty-six thousand, seven hundred three.
The standard form:
The standard form: 86,703.
The expanded form: 80,000 + 6,000 + 700 + 3.
Example 3: Write in the standard and word forms.
100,000 + 30,000 + 6,000 + 500 + 50
Solution:
The expanded form is,
100,000 + 30,000 + 6,000 + 500 + 50
The standard form: 136,550
The word form: One hundred thirty-six thousand, five hundred fifty.
Example 4: Use the number 700,000 + 5,000 + 20 + 1 to complete the check.
Solution:
The expanded form is,
700,000 + 5,000 + 20 + 1
The standard form: 705,021
The word form: Seven hundred five thousand, twenty one.
Example 5: Ava asks Liam and Mia to write “ninety-nine thousand, three hundred thirty-four” in the standard form. Who wrote the correct number? What mistake did the other make?
Solution:
The word form is ninety-nine thousand, three hundred thirty- four.
The standard form : 99,334
Therefore, Liam wrote the correct answer.
Mia has made a mistake in the tens place where instead of writing 3 she has written as 0.
The three forms to represent a number are:
The standard form: For example, 78,562.
The word form: For example, Six hundred fifty six.
The expanded form: For example, 500 + 20 + 3.
If there is a zero in between a number while writing the number in the expanded form or in the word form, the place is skipped.
The expanded form of a number helps us understand the place value of digits clearly. It also helps while comparing two or more numbers.