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- Scientific notation calculator

This calculator makes **conversion from scientific notation to decimal** and vice versa.
Also, the calculator can **multiply and divide numbers written in scientific notation**.
The calculator provides a full, step-by-step explanation for each operation.

**solution**

**explanation**

**Step 1.** Write entered numbers into the scientific notation.
(see **SN Converter** for detailed explanation)

**Step 2.** Divide numeric parts:

**Step 3.** Divide $10^{ 21 }$ by $10^{ 11 }$:

**Step 4.** Write the answer as the product of the numbers obtained
in steps 2 and 3:

working...

EXAMPLES

example 1:ex 1:

Convert number 73000000 into scientific notation.

example 2:ex 2:

Convert $8.32 \cdot 10^6$ to decimal notation.

example 3:ex 3:

Multiply numbers written in scientific notation
$$ 2.5 \cdot 10^{12} \, \cdot \, 3.42 \cdot 10^{-7} = $$

example 4:ex 4:

$$ \frac{8.5 \cdot 10^{24}}{2.41 \cdot 10^{18}} = $$

example 5:ex 5:

$$ \frac{3 \cdot 10^{-8}}{5.45 \cdot 10^{-6}} = $$

Find more worked-out examples in the database of solved problems..

**Scientific notation is a way of writing very large or very small numbers.**
In scientific notation, every number is represented as **a × 10 ^{n}**, where the decimal
number

In this example, we need to convert a number, which is greater than 10.
To do so move decimal point to the left until you get number
lesser than 10. Because the decimal is moved three places, we conclude that **n = 3**.

The result is:

$$ 7823.5 = 7.8235 \times 10^{\color{blue}{3}} $$In this example, there is no decimal point at the end of the number, so we will add one. Now, move the decimal point between the digits 7 and 8. Since the decimal is moved six places, we can conclude that n = 6.

The result is:

$$ 7800000 = 7.8 \times 10^{\color{blue}{6}} $$To convert the small number to scientific notation,
move the decimal point to the right (between digits 2 and 5).
Since the decimal was moved 8 spaces to the **right**, we might conclude that the n is -8.

The result is:

$$ 0.0000000254 = 2.54 \times 10^{\color{blue}{-8}} $$To multiply numbers written in scientific notation we first multiplay numeric parts,

1.2 * 3.45 = 4.14

After that, we multiply powers of 10.

10^{5} * 10^{-8} = 10^{5-8} = 10^{-3}

Putting everything together, we get:

$$ 1.2\cdot 10^5 \cdot 3.45 \cdot 10^{-8} = 4.14 10^{-3} $$Search our database with more than 250 calculators

RESOURCES

1. Writing Large and Small Numbers - with examples and solutions

2. Scientific Notation of Small Numbers

3. Multiplication and Division - video tutorial

439 640 687 solved problems