Scientific notation has been one of the oldest mathematical approaches.
If numbers are too big or too small, it can be simply calculated, using
scientific notations. Scientific notation is defined as a standard way of writing very large or very small numbers so that they are easier to compare and use in computations. |

**Changing from standard form to scientific notation**.

- Increase the power of ten by one, decimal point should be placed such that there is one non zero digit to the left of the decimal point.
- Count the number of decimal places the decimal has moved from the original number. This will be the exponent of 10.
- If the original number is less than one, exponent will be negative and if the original number is greater than one, exponent will be positive.

**Changing from scientific notation to standard form**.

- Exponents tells us how many places to move.
- For positive exponents of 10 move the decimal point to the right.
- For negative exponents of 10 move the decimal point to the left.

**Given below are the rules for scientific notation for addition, subtraction, multiplication and division.**

**Steps for adding numbers in scientific notation**

**Step1:**The given numbers should be written in scientific notation.

**Step 2:**Expand it to similar exponents only if the values of the exponents are not same, except the exponent portion if it is unchanged.

**Step 3:**Add the new coefficients.

**Step 4:**The coefficient should be between 1 and 10, if not convert again into scientific notation.

**Steps for subtracting numbers in scientific notation**

**Step 1:**Determine the number by which to increase the smaller exponent by so it is equal to the larger exponent.

**Step 2:**Increase the smaller exponent by this number and move the decimal point of the number with the smaller exponent to the left of the same number of places.

**Step 3:**Difference the new coefficients.

**Step 4:**The coefficient should be between 1 and 10, if not convert again into scientific notation.

**Steps for multiplying numbers in scientific notation**

**Step 1:**The coefficient of the given numbers should be multiplied.

**Example :**a * 10$^{b}$ * c * 10$^{d}$

**Step 2:**Add the numbers 10 to the power.

**Example :**ac * 10$^{b+d}$

**Step 3:**If the coefficient of the result is greater than 10, the result will be in the form ac * 10 $^{(b+d+1)}$

**Steps for dividing numbers in scientific notation**

**Step 1:**For the given problem difference the exponents of the base.

**Step 2:**With the subtracted new exponent write the number.

**Step 3:**Shift the decimal point to the right if the resulting number is less than 1, according to the decimal places shifted decrease the power. The result should be written in scientific notation.

**Example 1:** Write 622,000,000,000 in scientific notation

**Step 1: **Move the decimal place to the left.**For example:** we write 622,000,000,000 in decimal. The decimal point is
placed at the end of the number 622,000,000,000 and written as:

N = 6.22

**Step 2:** Now, determine how many times we moved the
decimal. In this example, we moved the decimal 11 times and as the
exponent is positive, in this we also move the decimal to left.
Therefore, a = 11, and so we get 10 $^{11}$.**Step 3:** Lastly, put the number in the correct form of scientific notation that is, N x 10$^{a}$ ,$\therefore$ 622,000,000,000 = 6.22 x 10 $^{11}$.

In this way, we write the scientific notation of any number.

**Example 2:** Convert 2.84 * 10$^6$ from scientific notation to standard notation**Solution:**

**Step 1:**Given 2.84 * 10$^6$ in scientific notation

Exponent = 6 (Positive)

**Step 2:** Move the decimal place 6 places to the right because exponent is positive

2.84 * 10$^6$ = 2.84 * 1,000,000 = 28,400,000

Example 3: Divide (0.27 x 10$^8$) by (3.2 x 10$^3$)**Solution:****Step 1:** Divide the decimal numbers

0.27 รท 3.2 = 0.084375**Step 2:** Subtract the powers of the base 10

8 - 3 = 5**Step 3:** Write the number with the subtracted new exponent

0.084375 x 10$^5$**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

0.084375 = 8.84375

0.08846 x 10$^{5}$ = 8.84375 x 10$^{3}$**Step 5:** Write the result in scientific notation

Hence, dividing scientific notation (0.27 x 10$^8$) by (3.2 x 10$^3$) we get 8.84375 x 10$^{3}$