Question

How do you write the number in scientific notation \[5,100,000\]?

Answer 1

Hint: Here, we will write the number as a product of two numbers or a multiple of 10 raised to a suitable power. A scientific notation is a way of expressing a number that is too large or too small in a simpler form or in the decimal form.

Formula Used:
We will use the following formula:
1. We can express the number \[N\] in the form of \[N = a \times {10^n}\] where \[1 \le a < 10\] and \[n\] is an integer.
2. Product rule of exponents: \[{a^m} \times {a^n} = {a^{m + n}}\]

Complete Step by Step Solution:
We are given with a number \[5,100,000\].
Let \[N\] be the given number. So, we get
\[N = 5,100,000\]
Now, we will rewrite the number of zeroes in the given number in the powers of \[10\]. So, we get
\[ \Rightarrow N = 51 \times {10^5}\]
We can express the number \[N\] in the form of \[N = a \times {10^n}\] where \[1 \le a < 10\] and \[n\] is an integer
Since the decimal point has to be moved a place to the left to convert it in the form of scientific notation, thus \[n = 1\]
\[ \Rightarrow N = 5.1 \times {10^5} \times {10^1}\] where\[a\] is greater than \[1\] and less than \[10\].
Product rule of exponents:\[{a^m} \times {a^n} = {a^{m + n}}\]
Now, by using the Product rule of exponents, we get
\[ \Rightarrow N = 5.1 \times {10^6}\]

Therefore, the scientific notation of \[5,100,000\] is \[5.1 \times {10^6}\].

Note:
Here, we will follow the following steps to write a decimal number in the form of scientific notation. First, we will move the decimal point such that there exists only one non-zero digit to the left of the decimal point and then we will count the number of digits between the old decimal point and the new decimal point. The number of digits gives the power of \[10\] that is equal to \[{10^n}\]. If the decimal point is moved to the left, then the exponent \[n\] is positive and if the decimal point is moved to the right, then the exponent \[n\] is negative. Thus these rules, we have to remember whenever we are writing a decimal number in scientific notation.