Question

How do you write\[100000\]in scientific notation?

Answer 1

Hint: To solve this question we need to know the relation between exponent terms and decimal points. Also, we need to know the relation between the direction of moving decimal points with positive exponent and negative exponent. We need to know the standard formula for scientific notation. We need to know the arithmetic operations like addition/ subtraction/ multiplication/ division.

Complete step-by-step solution:
In this question, we would find the scientific notation for\[100000\].
For that, we would know the standard formula for the scientific notation which is given below,
The basic standard formula for scientific notation is, \[M \times {10^n}\]
Where, \[1 \leqslant M \prec 10\]
Here\[M\]is the coefficient term.
In the given question we have,
\[100000\]
From the above term, we can see that there are five digits present after the term\[1\]. Let’s see an example
We know that\[10\]also can be written as\[{10^1}\]
\[10 = 10 \times 1 = {10^1}\]
(Here consider we have one zero in the term\[10\]. So, we put\[1\]in the power.)
As same as \[100\]can be written as\[{10^2}\]
\[100 = 10 \times 10 = {10^2}\]
(Here consider we have two zeros in the term\[100\]. So, we put\[2\]in the power)
In the question we have
 \[100000\]
We have\[5\]zeros in the above-mentioned term. So, we put\[5\]in the power as shown below,
\[100000 = 10 \times 10 \times 10 \times 10 \times 10 = {10^5}\]
According to the standard formula for scientific notation, \[{10^5}\]can also be written as,
\[100000 = {10^5} = 1 \times {10^5}\]
(Here\[M\]\[ = 1\])
So, the final answer is,
\[100000 = 1 \times {10^5}\]

Note: Note that we can check the final answer by expanding the power term\[({10^5} = 10 \times 10 \times 10 \times 10 \times 10 = 100000)\]. We would remember the standard formula for scientific notation. Note that if no term is mentioned in the exponent, we can take\[1\]in the exponent place\[\left( {10 = {{10}^1}} \right)\]. Also, note that when anything can be multiplied/divided\[1\], the final answer wouldn’t change. Note that\[{10^n}\]means we have to multiply the term\[10\]for\[n\]terms.