Question

How do you write $ 123456.789 $ in scientific notation ?

Answer 1

Hint: In order to write the given question $ 123456.789 $ into its scientific notation then , we need to first understand the term ‘ scientific notation ‘ . Scientific Notation is written in the form of $ a \times {10^n} $ , where $ 1 \leqslant a < 10 $ that is we can say the number has a single digit to the left of the decimal point where n is an integer . And the multiplication of a decimal by tens , hundreds and thousands or etc. itself means that the decimal will be moved to the right side by as many as the number of zeroes are there in the multiplier. If suppose that the decimal number having less digits after the decimal than the multiplier ( or the number of zero is more ) , then the extra zeroes must be added to the final answer as it is . If the decimal is being moved to the right, the exponent will be negative. By following these steps we can find the desired result of writing decimal when multiplying and making it in standard form.

Complete step-by-step answer:
 We have given a number in the form $ 123456.789 $
So, to calculate the scientific notation of the given , we have to first just sort that there must be a single digit to the left of the decimal point .
In order to do that we need to move the decimal point to the left side until one digit that 1 comes to the left of the decimal and 2 comes to the right of the decimal point.
Now the decimal point moves 5 places to the left from $ 123456.789 $ to $ 1.23456789 $ .But now the multiplier just used 5 zeroes to overcome the decimal and so we can write in scientific notation we have the $ {10^5} $ , as we know the fact that states If the decimal is being moved to the left , the exponent will be positive . That is now we have 5 zero after moving decimal to left and the exponent becomes $ {10^5} $ .
Therefore, the result is $ 1.23456789 \times {10^5} $ as we moved the decimal 5 place to the left
So, the correct answer is “ $ 1.23456789 \times {10^5} $ ”.

Note: . Do not Forget to verify the end of the result with the zeroes.
I. If you multiply a decimal with 10 , then the decimal point will be moved to the right side by 1 place .
II. If you multiply a decimal with 100 , then the decimal point will be moved to the right side by 2 places .
III. If you multiply a decimal with 1000 , then the decimal point will be moved to the right side by 3 places .
IV.If the decimal number has less digits after the decimal than the multiplier ( or the number of zero is more ) , then the extra zeroes must be added to the final answer as it is .
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive .
Also remember that any number for example – 150 is a number can also be expressed as 150.0 in the form of decimal .