Section 10.6: Writing Scientific Notation

Property

To convert from decimal notation to scientific notation:

1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
2. Count the number of decimal places, $n$, that the decimal point was moved.
3. Write the number as a product with a power of 10. If the original number is greater than 1, the power is $10^n$. If the original number is between 0 and 1, the power is $10^{-n}$.

Examples

• To convert 37,000, move the decimal 4 places to the left to get 3.7. Since the original number was greater than 1, the result is $3.7 \times 10^4$.

• To convert 0.0052, move the decimal 3 places to the right to get 5.2. Since the original number was between 0 and 1, the result is $5.2 \times 10^{-3}$.

Property

Scientific Notation
A number is expressed in scientific notation when it is of the form $a \times 10^n$ where $1 \le |a| < 10$ and $n$ is an integer.

How to Convert from Decimal to Scientific Notation

1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
2. Count the number of decimal places, $n$, that the decimal point was moved.
3. Write the number as a product with a power of 10. If the original number is greater than 1, the power of 10 will be $10^n$. If the number is between 0 and 1, the power will be $10^{-n}$.

Examples

• To write 8,300,000 in scientific notation, move the decimal 6 places to the left to get 8.3. So, the notation is $8.3 \times 10^6$.