Scientific Notation Tutorial
Part 2

Converting from Scientific Notation to Decimal Notation.

In order to convert a number written in scientific notation to one written in standard or decinal notation, follow these steps.

1. Write the number down without the "x 10^power" part.

2. Use the sign and numerical value of the exponent (power) to determine the direction and number of places to move the decimal place.

• Move the decimal point to the right if the exponent is positive.

• Move the decimal point to the left if the exponent is negative.

Remember, numbers with an exponent of 0 are between 1 and 10. Numbers with a positive exponent are greater than or equal to 10 while those with a negative exponent are between zero and 1.

Examples:

Convert 6.53 x 10⁴ into decimal (standard) notation.

• Write the number without the "x 10⁴" and add some extra zeros after in order to move the decimal point.
  6.53 x 10⁴ becomes 6.5300

• Since the exponent is positive, move the decimal 4 places to the right.
  6.53 x 10⁴ becomes 65300
  Notice that the decimal place doesn't actually appear in this case; it is understood to be at the end of the number. In science, however, placing a decimal point after the last zero in a number greater than or equal to 10 indicates that the zeros are significant figures. If I wrote the number as 65300., then I would have changed the number of signficant figures from 3 in the original number to 5.

Convert 2.50 x 10^-3 into decimal (standard) notation.

• Write the number without the "x 10^-3" part and put some extra zeros in front of the number.
  2.50 x 10^-3 becomes 0002.50
  

• Since the exponent is negative, move the decimal 3 places to the left.
  2.50 x 10^-3 becomes 0.00250
  Remember that the number should have the same number of significant figures as the original number.

Practice Problems

Convert the following numbers from scientific notation to standard (decimal) notation.

1. 3.0900 x 10³

2. 6.55 x 10^-5

3. 2.455 x 10²

4. 1.9 x 10^-4

5. 8.008 x 10²

6. 2.05 x 10^-3

Check answers