Question

Write the number 4 hundred thousand in scientific notation.

Answer 1

Hint: The format of writing a number in scientific notation is $a \times {10^b}$ where \[a\] is a number or decimal number such that the value of \[a\] lies between 1 and 10 & $b$ is the power of 10 so that the number written in the scientific notation is equal to the original number.

Complete step by step answer:
Firstly we write the number given in the question
Let ${\text{N}} = 400\;{\text{thousand}}$
Converting thousand into the number of zeros
$ \Rightarrow {\text{N}} = 400,000$
Now to convert this number ${\text{N}}$ into scientific notation we compare this number with
$ \Rightarrow {\text{N}} = a \times {10^b}$
And follow these points-
To write the number $a$ we put only one non zero number to the left most side of the whole number in our case that number $a\; = \;4$
Now we are left with $5$ zeros which means these trailing zeros will become the power of $b$.
After these steps our ${\text{N}}$ will look like this-
$ \Rightarrow {\text{N}} = 4 \times {10^5}$
This is the desired number written in the scientific notation.

Note: Scientific notation also known as standard form is a way of writing numbers to make it easy to use numbers with large values. So while dealing with these big numbers we write these in this form to work upon them easily.
Negative numbers and decimals can be converted to and for that we stick to one simple point i.e. keep only one number in the left most corner of the format putting decimal next to it and manipulate rest of the digits while using powers of $10$ to keep the number the same as before. For example if we want to convert the number $23456789$ into scientific notation we move in this manner-
${\text{N}} = 2345678 = 2.345678 \times {10^6}$
Here we have taken ${10^6}$ because after decimals there are $6$ digits and in this way we have converted the number into decimals.