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Dividing Scientific Notation

Scientific notation is the way of expressing very large or very small numbers in easiest form. Writing the numbers in the form of a x 10 n is called as scientific notation which is also known as exponential notation. Scientific notation is dividing numbers by a power of 10. To divide two numbers, simply divide the coefficients, and then subtract the exponent of the denominator from the exponent of the numerator.

Scientific notation has the following terms,

  • Co-efficient
  • Base
  • Exponent
Scientific notation should always have a base 10 and the base number 10 is always written in exponent form.

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How to Divide Scientific Notation?

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Let's see the steps of dividing scientific notation:

Step 1: The first step is to divide the decimal numbers present in the scientific notation numbers.

Step 2: Subtract exponents of the base (power of 10).

Step 3: Write the number with the subtracted new exponent.

Step 4: Check if the resulting number is less than 1 shift the decimal point to the right and then decrease the power according to the decimal places shifted.

Step 5: Write the result in scientific notation.

Dividing Scientific Notation Problems

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Solved Examples

Question 1: Divide (0.23 x 1011) by (2.6 x 104)
Solution:
 

Step 1: Divide the decimal numbers

0.23 ÷ 2.6 = 0.08846

Step 2: Subtract the powers of the base 10

11 - 4 = 7

Step 3: Write the number with the subtracted new exponent

0.08846 x 10 7

Step 4: Now the decimal number is less than 1, so right shift the decimal point by 2 places and decrease the power by 2

0.08846 = 8.846

0.08846 x 10 7 = 8.846 x 10 5

Step 5: Write the result in scientific notation

Hence, dividing scientific notation (0.23 x 1011) by (2.6 x 104) we get 8.846 x 10 5


 

Question 2: Divide 3.4 x 10 -3 by 5 x 10 6
Solution:
 

Step 1: Divide the decimal numbers

3.4 ÷ 5 = 0.68

Step 2: Subtract the powers of the base 10

- 3 - 6 = - 9

Step 3: Write the number with the subtracted new exponent

0.68 x 10 -9

Step 4: Now the decimal number is less than 1, so right shift the decimal point by 1 places and decrease the power by 1

0.68 x 10 -9 = 6.8 x10 -10

Step 5: Write the result in scientific notation

Hence, dividing scientific notation (3.4 x 10 -3) by (5 x 106) we get 6.8 x10 -10


 

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