Question

Express the following in the scientific notation:
A. 0.0048
B. 234,000
C. 8008
D. 500.0
E. 6.0012

Answer 1

Hint: The scientific notation is defined as the method for expressing the number which are too big or the number which are too small to be written conveniently in decimal form. In Britain it is referred to as a scientific form. The general form for writing formulas in scientific notation is $$N\times {10}^m$$. Here N is the coefficient or any real number, m is the exponent is an integer.

Complete step-by-step answer:
The rules for writing the number in scientific notation is that the scientific notation is written in two parts. The one is the digit with the decimal point which is placed after the first digit then followed by the multiplication with 10 to the power number of the decimal point that puts the decimal where it should be. If the number given to us is greater than 1 and multiple of 10 then the decimal point should be moved to the left and the power given to 10 or raised to 10 will be positive. But if the number is smaller than 1 then the power which is raised to 10 is negative and decimal would move to the right.
Now the (i) is 0.0048. Now first move the decimal place to the right to create a new number which exists between 1 to 10. So we get N = 4.8
So now we will determine the exponent which is the number of times we have moved the decimal. We have moved the decimal 3 times to right so the exponent will be negative. So m= -3 and we get $${10}^{-3}$$. Now substitute the values in the general formula we get $$4.8\times {10}^{-3}$$.
Now the (ii) is 234,000. Now first move the decimal place to the left to create a new number which exists between 1 to 10. So we get N= 2.34
So now we will determine the exponent which is the number of times we have moved the decimal. We have moved the decimal 5 times to the left so the exponent will be positive . So m= +5 and we get $${10}^5$$. Now substitute the values in the general formula we get$$2.34\times {10}^5$$.
Now the (iii) is 8008. Now first move the decimal place to the left to create a new number which exists between 1 to 10. So we get N= 8.008
So now we will determine the exponent which is the number of times we have moved the decimal. We have moved the decimal 3 times to the left so the exponent will be positive . So m= +3 and we get$${10}^3$$. Now substitute the values in the general formula we get $$8.008\times {10}^3$$.
Now the (iv) is 500.0. Now first move the decimal place to the left to create a new number which exists between 1 to 10. So we get N= 5.000
So now we will determine the exponent which is the number of times we have moved the decimal. We have moved the decimal 2 times to the left so the exponent will be positive . So m= +2 and we get $${10}^2$$. Now substitute the values in the general formula we get $$5.000\times {10}^2$$
Now the (v) is 6.0012. Now here the Nis itself present between 1 to 10. So it is itself in its scientific notation form.

Note: We can change the scientific notation into the standard form by just multiplying it by its power raised to 10. The use of scientific notation is done in complex concepts such as polynomials and exponents. It is used in representing the population of the world or the number of cells present in the body and also representing the mass of dust particles.