Question

How do you write $ \left( {1.5 \times {{10}^5}} \right) - \left( {8 \times {{10}^4}} \right) $ in expanded form?

Answer 1

Hint: : In order to the expression in the standard form , first we have to convert both the terms into their standard form , then apply the operation of subtraction to calculate the answer. Since in both the terms the exponent value is positive so shift the decimal point of the number toward the right side up to places equal to the exponent value. Apply the subtraction operator to get the required result.

Complete step-by-step answer:
We have given an expression having two terms having operation in between them
 $ \left( {1.5 \times {{10}^5}} \right) - \left( {8 \times {{10}^4}} \right) $ ----(1)
Since both the given in the above expression are in the scientific notation and before doing the operation, we have to convert them both in the standard form.
Let's take the first term first $ \left( {1.5 \times {{10}^5}} \right) $
As we can clearly see that the exponent value of the 10 is positive i.e. 5 and when the power of 10 is positive then the decimal point of the number get shifter towards right sides up to places equal to the value of exponent
Here the exponent value is 5 so we have to shift the decimal of $ 1.5 $ towards the right side up to 5 places to obtain the expanded form. Then we get
 $ = 150000 $
Similarly following the same steps for the second term, the value of exponent in this case is 4 and decimal number is 8
So the expanded form is $ 80000 $
Now putting these standard forms in the original expression , we get
 $
   = 150000 - 80000 \\
   = 70000 \;
  $
Therefore, the Standard of the expression $ \left( {1.5 \times {{10}^5}} \right) - \left( {8 \times {{10}^4}} \right) $ is equal to $ 70000 $ .
So, the correct answer is “ $ 70000 $ ”.

Note: Do not Forget to verify the end of the result with the zeroes .
I.If you multiply a decimal with 10 , then the decimal point will be moved to the right side by 1 place .
II.If you multiply a decimal with 100 , then the decimal point will be moved to the right side by 2 places .
III.If you multiply a decimal with 1000 , then the decimal point will be moved to the right side by 3 places .
IV.f the decimal number having less digits after the decimal than the multiplier ( or the number of zero is more ) , then the extra zeroes must be added to the final answer as it is .
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.