Question

Express the following numbers in standard form:
3,18,65,00,000

Answer 1

Hint: In this question, we need to write the number as the sum of its place values. Then expand correspondingly to get the standard form of the given number.

Complete step-by-step answer:
FACE VALUE AND PLACE VALUE OF THE DIGITS:
In a numeral, the face value of a digit is the value.
In a numerical, the place value of a digit changes according to the change of its place.

Let us now consider the given number in the question.
3,18,65,00,000
Now the face value of the digit 3 is 3 and its place value is given by
\[3\times 1000000000\]
Let us now consider the next digit 1 whose face value is 1 and place value is given by
\[1\times 100000000\]
Now, for the next digit 8 the face value is 8 and its place value is given by
\[8\times 10000000\]
Let us now consider the next digit 6 whose face value is 6 and its place value is given by
\[6\times 1000000\]
Now, on considering the next digit 5 its face value is 5 and its place value is given by
\[5\times 100000\]
Let us now consider the next digit 0 whose face value is 0 and place value is given by
\[0\times 10000\]
Now, for the next digit 0 the face value is 0 and its place value is given by
\[0\times 1000\]
Let us now consider the next digit 0 whose face value is 0 and its place value is given by
\[0\times 100\]
Now, on considering the next digit 0 its face value is 0 and its place value is given by
\[0\times 10\]
Let us now consider the next digit 0 whose face value is 0 and place value is given by
\[0\times 1\]
Now, the standard form of the given number is
\[3\times 1000000000+1\times 100000000+8\times 10000000+6\times 1000000+5\times 100000\]
Thus, it can also be written as
\[3.1865\times {{10}^{9}}\]

Note: It is important to note that to write the standard form we first need to write its place value accordingly. If there are zeros then its place value will be 0 itself and contributes nothing to the number other than 0.
It is also to be noted that while writing the place value the number of zero to be placed or multiplied with the number should be checked carefully because neglecting any one of the 0 changes the place value of the digit completely and so the standard form and the number itself.