Scientific notation is a way to write very large or small numbers in their simplest form. It involves writing a number as the product of a coefficient and a power of 10. To divide numbers in scientific notation, you divide the coefficients, subtract the exponents, shift the decimal if needed to keep the coefficient between 1 and 10, and write the result with the new exponent. Some examples of dividing numbers in scientific notation are worked out step-by-step. The document also provides practice problems for dividing numbers in scientific notation and examples of using scientific notation to solve real-world problems involving distances and speeds.

1. Dividing
Scientific
Notation

2. Scientific notation is the way of expressing
very large or very small numbers in easiest
form.
Writing the numbers in the form a x 10ᵑ
of is called Scientific Notation which is
also known as Exponential Notation.
Scientific Notation has the following terms
• Co-efficient
• Base
• Exponent

3. Scientific Notation should always have a base
10 and the base number 10 is always written in
exponent form. The number 123, 000, 000,
000 in scientific notation is written as;
1.23 x 10¹¹
The first number 1.23 is called the co-
efficient. It must be greater than or equal 1
and less than 10.
The second number is the base. It must
always be 10 in scientific notation. The base
number 10 is always written in exponent form.
In the number 1.23 x 10¹¹ the number 11 is
referred to as the exponent or power of ten.

4. How to divide scientific
notation ?
Step 1: Divide the coefficient.
Step 2: Subtract exponent 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 & then decrease the
power according to the decimal places shifted.
Step 5: Write the result in scientific notation.

5. Question 1: Divide (0.23 x 1011) by (2.6 x 104)
Solution: Step 1: Divide the coefficient.
0.23 ÷ 2. = 0.08846
Step 2: Subtract the exponent of the base 10
11 – 4 = 7
Step 3: Write the number with the subtracted new exponent
0.08846 x 10⁷
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 x 10⁷ = 8.846 x 10⁵
Step 5: Write the result in scientific notation.
Hence, dividing scientific notation (0.23 x 1011) by (2.6 x) we get
8.846 x 10⁵

6. Question 2: Divide 3.4 x 10 -3 by 5 x 10 6
Solution :
Step 1: Divide the coefficient.
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 x 10 ⁻¹⁰
Step 5: Write the result in scientific notation.
Hence, dividing scientific notation ( 3. 4 x 10 ⁻ᶟ) by ( 5 x 10⁻⁶)
we get 6.8 x 10 ⁻¹⁰

7. Try this:
1. (9 x 10⁻⁶)/(3 x 10⁻ᶟ)
2. (2 x 10ᶟ) ÷ (4 x 10⁸)
3.
4. (3 x 10⁻⁶) ÷ ( 2 x 10⁻⁴)
5. (7 x 10⁻⁵)/(2 x 10¹⁰)

8. Problems:
1.) What is the ratio of Milky Way radius
to our solar system radius given that, the
distance from Pluto to Sun is 5.9 x 10¹² meters
and the Milky Way disk radius is 3. 9 x 10²⁰
meters.
Round the coefficient to the nearest tenth.
2.) The speed of light is 3 x 10⁸
meters/seconds. If the sun is 1.5 x10¹¹ meters
from the Earth, how many seconds does it
take light to reach the earth?

9. Prepared by:
Raylin Dayang