Question

Which of the following represent the number \[300,000,000\]
A. \[3 \times {10^6}\]
B. \[3 \times {10^7}\]
C. \[3 \times {10^8}\]
D. \[3 \times {10^9}\]
E. \[3 \times {10^{ - 9}}\]

Answer 1

Hint: This question involves the arithmetic operations like addition/ subtraction/ multiplication/ division. We need to know the relation between the decimal point and the term present in the ten to the power. Also, we need to know how to expand the power terms to check whether the final answer is correct or wrong.

Complete step by step solution:
In this question, we would find the term which represents the number \[300,000,000\].
Before that, we need to know the relation between the decimal point and the term which is present in the ten to the power.
When we move the decimal point from left to right the number present in the ten to the power will decrease.
Let’s take the number \[100\]
It also can be written as,
\[100.00 \times {10^0} \to \left( 1 \right)\]
(We know that anything power zero will be\[1\])
Let’s move the decimal point from left to right, we get
\[1000.0 \times {10^{ - 1}} \to \left( 2 \right)\]
The same as, when we move the decimal point from right side to left side the number which presents in the ten to the power will increase.
Let’s take the equation\[\left( 2 \right)\]
\[\left( 2 \right) \to 1000.0 \times {10^{ - 1}}\]
Let’s move the decimal point from the right side to the left side, we get
\[100.00 \times {10^0} \to \left( 3 \right)\]
By using this procedure we can easily simplify the given term in the question.
We have\[300,000,000\]
It also can be written as,
\[300,000,000.0 \times {10^0}\]
Let’s move the decimal point from right to left for eight digits, we get
\[3.00,000,000 \times {10^8}\]
It also can be written as,
\[3 \times {10^8}\]
We move eight-digit, so the number which presents in the ten to the power will increases for each one movement of the decimal point as follows,
\[{10^0} \to {10^1} \to {10^2} \to {10^3} \to {10^4} \to {10^5} \to {10^6} \to {10^7} \to {10^8}\]
So, the final answer is,
\[300,000,000 = 3 \times {10^8}\]

So, the correct answer is “Option C”.

Note: Note that when we move the decimal point from the left side to the right side, the number present in the ten to the power will be decreased for each one movement of the decimal point. Also, note that when we move the decimal point from right side to left side, the number present in the ten to the power will be increased for each one movement of the decimal point.