Question

How do you write 78,000 in scientific notation?

Answer 1

Hint: Scientific notation is a method of writing very large numbers or small numbers in a short form. We write scientific notation by some number from 1 to 10 multiplied by the power of 10 such that the result is equal to the original number. For example scientific notation of 20 is $2\times {{10}^{1}}$ , scientific notation of 2345 is $2.345\times {{10}^{3}}$. We just divide the number by the power of 10 such that the quotient is between 1 to 10 then multiply it with the power of 10.

Complete step-by-step solution:
To write a scientific notation of a number we write a number between 1 to 10 multiply it with a power of 10 such that the resulting notation will be equal to the number. So to do that we first have to divide the number by some power of 10 such that the quotient will be between 1 to 10 then multiply with a power of 10.
For example, we have to find the scientific notation of 16754 first we have to divide 16754 by some power of 10 such that the result is between 1 to10. So the answer would be${{10}^{4}}$. If we divide 16754 by ${{10}^{4}}$ then the result is 1.6754. Then we can multiply with${{10}^{4}}$. That means the answer is $1.6754\times {{10}^{4}}$.
So we can write
$16754=\dfrac{16754}{{{10}^{4}}}\times {{10}^{4}}$
$\Rightarrow 16754=1.6754\times {{10}^{4}}$
In our case, we have to find the scientific notation of 78,000 we have to divide 78,000 with a power of 10 such that the quotient is between 1 to 10 then multiply with it. The divisor will be ${{10}^{4}}$.
$78,000=\dfrac{78,000}{{{10}^{4}}}\times {{10}^{4}}$
$\Rightarrow 78,000=7.8\times {{10}^{4}}$(Ans)

Note: Another shortcut method to write in scientific notation of x is if $x > 1$ or $x < -1$ then we can simply put a decimal sign in between ${{1}^{st}}$ and ${{2}^{nd}}$ number from left then multiply with 10 to the power the total number of digits between original and new decimal . If $x < 1$ or $x > -1$ then the decimal sign would be between ${{1}^{st}}$ and ${{2}^{nd}}$ from right then multiply with 10 to the power minus of total number of digits between original and new decimal.