Question

How do you write $0.000043$ in scientific notation ?

Answer 1

Hint: In order to write the given question $0.000043$ 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 solution:
We have given a decimal number in the form $0.000043$ where after decimal there are 6 digits .
Here, in this question we have given decimal as $0.000043$.
So , to calculate the scientific notation of the given decimal , 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 right side until one digit that 4 comes to the left of the decimal and 3 comes to the right of the decimal point .
Now the decimal point moves five places to the right from $0.000043$ to $4.3$ . 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 right, the exponent will be negative . That is now we have 5 zeros after moving decimal to right and the exponent becomes ${10^{ - 5}}$ .
Hence , the result is $4.3 \times {10^{ - 5}}$ as we moved the decimal 5 places to the right .

Note:
1. Do not Forget to verify the end of the result with the zeroes .
2. If you multiply a decimal with 10 , then the decimal point will be moved to the right side by 1 place
3. If you multiply a decimal with 100 , then the decimal point will be moved to the right side by 2 places .
4. If you multiply a decimal with 1000 , then the decimal point will be moved to the right side by 3 places .
5. 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.