**What are Scientific Notations?**

A scientific notation is a form of writing a given number, an equation, or an expression in a form that follows certain rules. In other words, Scientific notation is the standard way to express a number as the product of a real number and power of 10.

**Addition and Subtraction of Numbers in Scientific Notations**

The following steps are involved for the addition of numbers in scientific notations –

- Rewrite the number with the smaller exponent so that it has the same exponent as the number with the larger exponent by moving the decimal point of its decimal number.
- Add / Subtract the decimal numbers. The power of 10 will not change.
- Convert your result to scientific notation if necessary.

Let us understand the above steps using an example.

**Example**

Suppose we have two numbers 7 . 3 x 10 ^{4} and 2 . 4 8 x 10 ^{5}

We want to find the sum of these numbers. Let us see how it can be done.

**Solution**

We will have, ( 0 . 7 3 x 10 ^{5} ) + (2 . 4 8 x 10 ^{5 })

= ( 0. 7 3 + 2 . 4 8 ) x 10 ^{5}

= 3 . 2 1 x 10 ^{5}

**Example**

Suppose we have two numbers 4 . 9 x 10 ^{3} and 1 . 3 x 10 ^{4}

We want to subtract the second number from the first number. Let us see how it can be done.

**Solution**

We will have, ( 4 . 9 x 10 ^{3} ) – (1 . 3 x 10 ^{4} )

= ( 0 . 4 9 x 10 ^{4} ) – (1 . 3 x 10 ^{4} )

= ( 0 . 4 9 – 1 . 3 ) x 10 ^{4}

= – 0 . 8 1 x 10 ^{4}

**Multiplication and Division of Numbers in Scientific Notations**

Multiplication of numbers in scientific notation is different from their addition and subtraction. The following steps are involved for the multiplication of numbers in scientific notations –

- Obtain the decimal numbers in scientific notation.
- Multiply / divide the decimal numbers.
- Multiply / divide the powers of 10 by adding their exponents.
- Convert your answer to scientific notation if necessary.

Let us understand the above steps using an example.

**Example**

Suppose we have two numbers ( 3 . 4 x 10 ^{– 2} ) and ( 6 . 2 x 10 ^{6} ) and we want to find their product.

**Solution**

We will have, 3 . 4 x 6 . 2 = 2 1 . 0 8 …………………………. ( 1 )

Next, we will multiply the powers of 10 for which we need to add the exponents of the two decimal numbers. 10 ^{– 2} x 10 ^{6} = 10 ^{– 2 + 6 } = 10 ^{4} ………………………….. ( 2 )

From ( 1 ) and ( 2 ) we will have,

( 3 . 4 x 10 ^{– 2} ) x ( 6 . 2 x 10 ^{6} ) = 2 1 . 0 8 x 10 ^{4}

We will then have, 2 1 . 0 8 x 10 ^{4} = 2 . 1 0 8 x 10 ^{5}

**Hence, ( 3 . 4 x 10 **^{– 2}** ) x ( 6 . 2 x 10 **^{6}** ) = 2 . 1 0 8 x 10 **^{5}

**Example**

Suppose we have two numbers ( 8 . 4 x 10 ^{5} ) and ( 1 . 4 x 10 ^{– 2 } ) and we want to divide the first number by the second.

**Solution**

We will have, 8 . 4 ÷ 1 . 4 = 6 ………………….. ( 1 )

( 10 ^{5} ) ÷ ( 10 ^{– 2} ) = 10 ^{( 5 – ( – 2 )} = 10 ^{5 + 2} = 10 ^{7} …………………………. ( 2 )

Now, we will combine the results obtained in ( 1 ) and ( 2 ) to get,

( 3 . 4 x 10 ^{– 2} ) ÷ ( 6 . 2 x 10 ^{6} ) = 6 x 10 ^{7}

Hence, **( 3 . 4 x 10 **^{– 2}** ) ÷ ( 6 . 2 x 10 **^{6}** ) = 6 x 10 **^{7}

**Using the scientific notation calculator**

It is quite simple to use the scientific notation calculator for performing operations involving scientific notations. The following steps are required to be followed for this purpose –

**Step 1** – The first step is to enter the details of the two scientific notations on whom an operation is to be performed. Let us take, for example, ( 3 . 4 x 10 ^{– 2} ) and ( 6 . 2 x 10 ^{6} ) to perform different operations using the calculator. So, in the first step, we will enter the first number in the box against the “ 1^{st} number “ in the Enter Information “ section of the calculator. Below is the snapshot providing detail of how the 1^{st} number will be entered –

Note here that both the decimal value and the power of 10 need to be entered separately.

**Step 2** – The next step is to enter the second number in the box against the “ 2^{nd} number “ in the Enter Information “ section of the calculator. We will therefore enter 6 . 2 x 10 ^{6} as the second number. Below is the snapshot providing detail of how the 2^{nd} number will be entered –

**Step 3** – after entering both the numbers, we need to mention the operation we wish to perform between them. we shall select “ + “ , “ – “, “ x “ or “ ÷ “ from the drop-down menu of the operation box. Let us, for example, multiply the two numbers. We will therefore choose the “ x “ option from the drop-down menu. Below is the snapshot of what the selection would look like –

**Step 4** – Now that we have entered all the required information, our last step is to perform the calculation. For this purpose, we just need to click on the “ calculate “ button. As soon as we will click on this button, we can see the result obtained on the right-hand side of the values that we had entered in the previous steps. Below is a snapshot of how the selection would look like when we will click on the “ calculate “ button

In this manner, using this scientific notation calculator, we can perform all the operations involving scientific notations.