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# Scientific notation calculator

This scientific notation converter/calculator makes a conversion between scientific and decimal notation, and performs arithmetic operations on scientific numbers. The calculator can multiply, divide, and evaluate powers of numbers written in scientific notation.

Multiply and divide scientific numbers
input two numbers and select an opertion
help ↓↓ examples ↓↓
 X = × 10 Y = × 10 Example: X=12×10^3  Y=2.15×10^-12
 X = E Y = E Example: X=12E-10  Y=15E8
 X = Y = Example: X=12000000  Y=0.000000042
 Find: X×Y X/Y X^2 X^
Scientific Notation Converter
convert scientific notation to decimal and back
help ↓↓ examples ↓↓
52E-7
0.00000042
working...
EXAMPLES
Question 1:ex 1:
Multiply numbers written in scientific notation $$2.5 \cdot 10^{12} \, \cdot \, 3.42 \cdot 10^{-7} =$$
Question 2:ex 4:
$$\frac{8.5 \cdot 10^{24}}{2.41 \cdot 10^{18}} =$$
Question 3:ex 3:
Convert number 73000000 into scientific notation.
Question 4:ex 4:
Convert $8.32 \cdot 10^6$ to decimal notation.
example 5:ex 5:
$$\left( 3 \cdot 10^{-8} \right)^{12}=$$
Find more worked-out examples in our 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.

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.

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.

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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