Question

How do you write $ 3.6 \times {10^8} $ in standard form?

Answer 1

Hint: Here first of all we will take the given expression and will convert it into the normal form. It is also known as the ordinary form. Here we will convert by placing seven zeros after the first term.

Complete step-by-step solution:
Observe the given number and power of $ 10 $
Here given that the power to \[10\] is $ (8) $
Step 2 Write as the multiplication of $ 10 $ eight times.
\[3.6 \times {10^8} = 3.6 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10\]
Step 3 Do the multiplication by $ 10 $ one at a time
\[
  3.6 \times {10^8} = 36 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \\
  3.6 \times {10^8} = 360 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \\
  3.6 \times {10^8} = 3600 \times 10 \times 10 \times 10 \times 10 \times 10 \\
  3.6 \times {10^8} = 36000 \times 10 \times 10 \times 10 \times 10 \\
  3.6 \times {10^8} = 360000 \times 10 \times 10 \times 10 \\
  3.6 \times {10^8} = 3600000 \times 10 \times 10 \\
  3.6 \times {10^8} = 36000000 \times 10 \\
  3.6 \times {10^8} = 360000000 \\
 \]
This is the required solution.

Alternative method: Here we are given the product of two terms expressed in the form of \[a \times {10^b}\]and compare with the given expression, $ 3.6 \times {10^8} $
\[ \Rightarrow a = 3.6\,\]
And $ b = 8 $
Here we will write seven zeros after the number six, since we have one digit after the decimal point therefore the number of zeros will be equal to eight minus one.

Additional Information: Also, remember the difference between the ordinary number and ordinal number. Ordinal number is the number which tells the position of the object or something in the list. For Example first, second, third, etc. It simply tells us the rank or the position of something in the group. Whereas, the ordinary numbers are the numbers which include whole numbers, rational, irrational numbers and real and imaginary numbers.

Therefore, the correct answer is $ 360000000 $ .

Note: In case of having positive power to ten, simply write zeros after the number. If number two is given to the power ten, then write two zeros after the number while in case of negative power, you have to divide and have to move the decimal point right to left and you have to remove the number of zeros.