Question

How do you write 6,580,000,000,000,000,000,000 in scientific notation?

Answer 1

Hint: Scientific notation is a method expressing numbers in terms of a decimal number between 1 and 10, but not 10 itself multiplied by a power of 10. In scientific notation, all numbers are written in the general form as $N \times {10^m}$. N times ten raised to the power of m, where the exponent m is an integer, and the coefficient N is any real number. The integer m is called the order of magnitude and the real number N is called the significant.

Complete step-by-step solution:
In this question, we want to write 6,580,000,000,000,000,000,000 in scientific notation.
As we already know the general form is $N \times {10^m}$.
The first step is to move the decimal place to the left to create a new number from 1 to 10.
Here, 6,580,000,000,000,000,000,000 is a whole number, the decimal point will be given at the end of the number 6,580,000,000,000,000,000,000. So, we get N=6.58.
The second step is to determine the exponent, it will be the number of times you moved the decimal.
Here, we moved the decimal 21times and because we moved the decimal to the left, the exponent is positive. Therefore, m=11.
The third step is to put the value of N and m in the general form of the scientific notation.
Therefore, we get $6.58 \times {10^{21}}$.

Hence, the scientific notation of the given number 6,580,000,000,000,000,000,000 is $6.58 \times {10^{21}}$.

Note: The scientific notation rules:
The scientific notations are written in two parts. One is the digits, with the decimal point placed after the first digit, followed by multiplication with 10 to the power number of the decimal point that puts the decimal point where it should be.
If the given number is greater than 1 and multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive.
If the given number is smaller than 1 means in the form of decimal numbers, then the decimal point has to move to the right, and the power of 10 will be negative.