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Scientific notation calculator

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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.

Divide $ 5.2\cdot 10^{21} $ by $ 4\cdot 10^{11} $.

solution

$$ \frac{ 5.2\cdot 10^{21} }{ 4\cdot 10^{11} } = 1.3\cdot 10^{10} $$

explanation

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

$$ 5.2\cdot 10^{21} = 5.2\cdot 10^{21} $$$$ 4\cdot 10^{11} = 4\cdot 10^{11} $$

Step 2. Divide numeric parts:

$$ \frac{ 5.2 }{ 4 } = 1.3 $$

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

$$ \frac{ 10^{ 21 } }{ 10^{ 11 } } = 10^{ 21 - 11 } = 10^{ 10 } $$

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

$$ 1.3 \cdot 10^{ 10 } $$

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Script name : scientific-notation-calculator

Form values: 1 , 5.2e21 , 2 , 4e11 , 1 , g , Divide $ 5.2\cdot 10^{21} $ by $ 4\cdot 10^{11} $. , ,

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Scientific Notation Converter
convert scientific notation to decimal and back
help ↓↓ examples ↓↓
52 E-7
0.00000042
Multiply and divide scientific numbers
input two numbers and select an opertion help ↓↓ examples ↓↓
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

Scientific notation is a way of writing very large or very small numbers. In scientific notation, every number is represented as a × 10n, where the decimal number a is greater than 1 and lesser than 10. We will provide some examples of how to convert numbers to scientific notation.

Convert 7823.5 to scientific notation

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.

Converting big number to scientific notation

The result is:

$$ 7823.5 = 7.8235 \times 10^{\color{blue}{3}} $$

Convert 7800000 to scientific notation

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.

Converting big number to scientific notation

The result is:

$$ 7800000 = 7.8 \times 10^{\color{blue}{6}} $$

Convert 0.00000254 to scientific notation

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.

Converting small number to scientific notation

The result is:

$$ 0.0000000254 = 2.54 \times 10^{\color{blue}{-8}} $$

Multiply $1.2 \cdot 10^5 $ by $3.45 \cdot 10^-8$

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.

105 * 10-8 = 105-8 = 10-3

Putting everything together, we get:

$$ 1.2\cdot 10^5 \cdot 3.45 \cdot 10^{-8} = 4.14 10^{-3} $$
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