Question

How do you write $5.2\times {{10}^{3}}$ in standard form?

Answer 1

Hint: The standard form of a number is the easiest way to express the number. We will make the number exponent free by expanding it. Then we will multiply the non-zero digits. We will write the zeros in the right end. If the number is a decimal number, then we will count the number of digits after the decimal point. Then we will use the zeros in the numbers to remove the decimal point.

Complete step by step answer:
Let us consider the given problem.
We are asked to write $5.2\times {{10}^{3}}$ in standard form.
Now, we need to make the number exponent free by expanding the given number.
We have the number ${{10}^{3}}$ in the given problem.
Let us make this exponent free by expanding it as ${{10}^{3}}=1000.$
Now the number in the question becomes $5.2\times {{10}^{3}}=5.2\times 1000.$
Since one of these numbers to be multiplied is a decimal number, we need to remove the decimal point to make the number in its standard form. We can do it by using the zeros in the number $1000.$
We have only one digit after the decimal point. So, we need only one zero to remove the decimal point. Since $1000=100\times 10,$ we will multiply $5.2$ with $10$ and we will get $5.2\times 10=52.$
Now the given number will become $5.2\times {{10}^{3}}=52\times 100.$
When we multiply two numbers, we multiply the non-zero digits first and then write the zeros at the right end of the number.
So, we first multiply $52$ with $1$ and then write the two zeros at the right end.
We will get $52\times 100=5200.$

Hence the standard form of $5.2\times {{10}^{3}}=5200.$

Note: We usually use the standard form of the numbers in daily life. But, when we need to deal with large numbers, it will be easy to use the scientific notation. For example, the Avogadro number is $6.022\times {{10}^{23}}.$