Question

How do you write $ 512 $ in scientific notation?

Answer 1

Hint: Scientific notation: Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
Calculating the scientific notation for a positive integer as simple that, as it always follow this notation: $ a \times {10^b} $

Complete step by step solution:
As we have to find scientific notation for a given number.
We will go step by step:
Step 1: To find $ a, $ pick the number and move a decimal place to the correct position.
Original Number: $ 512 $
New Number: $ 5.12 $
Step 2: Now, we will find $ b, $ count how many places to the right of the decimal.
New Number: $ 5.\,\,1\,\,2 $
Decimal count: $ \,\,\,1\,\,2 $
There are two places to the right of the decimal place.
Step 3: Now we can reconstruct the number into the scientific notation, with the help of as we know.
Remember, the notation is: $ a \times {10^b} $
  $ a = 5.12 $
  $ b = 2 $
Now the whole thing:
  $ 5.12 \times {10^2} $
Step 4: We can check our work:
  $ {10^2} = 100 \times 5.12 = 512 $
So, the correct answer is “ $ 5.12 \times {10^2} $ ”.

Note: Scientific notation is used to write very large numbers or very small numbers using less digits. As we know about the distance of earth from the sun. It is too large to write if we write it in simple notation. So, we write in scientific notation and make it shorter. In experimental data it is widely used to make units and observations readable and easily memorable.