Question

The distance of the earth from the sun is 149,000,000 km. In scientific notation the distance is:
A.\[\;149 \times {10^6}km\]
B. \[14.9 \times {10^7}km\]
C. \[1.49 \times {10^8}km\]
D. \[0.149 \times {10^9}km\]

Answer 1

Hint: First we’ll understand the scientific notation and how any number can be converted into the form of scientific notation i.e. in the form of $N \times {10^a}$, where $1 \leqslant \left| N \right| < 10$ and ‘a’ is an integer. Using all these we’ll find the scientific notation for 149,000,000

Complete step by step Answer:

Given that, the distance of the earth from the sun is 149,000,000 km.
Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power.
The form of scientific notation is $N \times {10^a}$, where $1 \leqslant \left| N \right| < 10$ and ‘a’ is an integer
There are some step to make any number into scientific notation i.e.
(1) Move the decimal to the right or left to create a number N, $1 \leqslant \left| N \right| < 10$
(2) Determine the exponent, which is the number of times we moved the decimal, if left then the exponent will be positive, and if right the exponent will be negative.
(3) Put the number in the correct form for scientific notation.
Now using the above method we get as
149,000,000 can also be written as
\[ = 149 \times 100,0000\]
\[ = 1.49 \times 100,000,000\]
\[ = 1.49 \times {10^8}\]
Therefore if the distance of the earth from the sun is 149,000,000 km, in scientific notation the distance is \[1.49 \times {10^8}\] km.
Hence, option (C) is correct.

Note: In the above solution we mentioned in the step that the power of 10 depends on whether the decimal is shifted towards the right of left so always keep that in mind as the maximum chances of getting an error is this step only. If there are too many zeros you can write the number in scientific notation, it will give you a better visualization and it will also decrease the error rate, as when there are many zeros in an expression we tend to miss some of them, getting incorrect answers.