Question

How do you use scientific notation to express the number 355000 to one significant figure?

Answer 1

Hint: The number given above (i.e. 355000) has 3 significant figures and we are asked to express this number using scientific notation in such a way so that it has only one significant figure. This can be done by rounding off the given number. Rounding off the given number will give 400000. Then write this given number into scientific notation.

Complete step by step solution:
The number given in the above problem which we have to make it to one significant figure:
355000
As you can see in the above number, 3 significant figures are there (i.e. 3, 5 and 5). So, to convert this number in such a way so that we get one significant figure, we are going to round off the given number.
Rounding off the given number we get,
400000
Now, we are going to convert the above number into scientific notation by writing this number into product of two numbers in such a way so that first part of the number should lie between 1 to 10 and the second part contains some power of 10 and the power is adjusted in such a way so that we will restore our original number.
Putting a decimal between 4 and 0 we get,
$\Rightarrow 4.00000$
As we have shifted the decimal five places from the last number so we have to multiply 10 to the power of 5 to the above number.
$\Rightarrow 4\times {{10}^{5}}$
Now, the significant figure in the above number is 1. Hence, we have converted the given number into one significant figure.

Note: To solve the above problem, you need to know how to count the significant figures in any number. Also, you should know how to round off any number. Now, you may think that why we have rounded off the above number to 400000 because if we have rounded off the above number to say 360000 then the significant figures we will get is 2 (i.e. 3 and 6) and we want only one significant figure.