Question

How do you write $ 6 \times {10^3} $ in standard notation?

Answer 1

Hint: The method of expressing too large or too small numbers in the decimal form for a convenient expression is called scientific notation. In scientific notation, a number is written as a product of a number lying between 1 and 10 and a power of 10. For example, $ N \times {10^m} $ is a scientific notation where N lies between 1 and 10 and involves only significant figures. so while converting the scientific notation into standard notation we simply multiply the decimal number with the power of 10, in the given question, there is no decimal involved so the calculation is easy and we have to write $ {10^3} $ in simplified form and then multiply it with the number 6. Using this information, we can find out the correct answer.

Complete step-by-step answer:
Given,
 $ 6 \times {10^3} $
 $ {10^3} $ means 10 multiplied with itself 3 times, so –
 $
  {10^3} = 10 \times 10 \times 10 \\
   \Rightarrow {10^3} = 1000 \;
  $
So
 $
  6 \times {10^3} = 6 \times 1000 \\
   \Rightarrow 6 \times {10^3} = 6000 \;
  $
Hence, we can write $ 6 \times {10^3} $ in standard notation as $ 6000 $ .
So, the correct answer is “ $ 6000 $ ”.

Note: While writing a number in scientific notation, we first write the digits with decimal, the decimal point is placed after the first digit and the digits after the decimal point are rounded off so that the number of digits is equal to the significant figures followed by the multiplication with 10 raised to the power number of digits that decimal places is moved. The given number is written in scientific notation and we have to convert it into the standard notation so we follow the inverse process. This way we can solve all the questions similar to this one.