Scientific Notation Converter

Convert a number to and from scientific notation, e notation, engineering notation, standard form, and real numbers. Enter a number or a decimal number or scientific notation and the calculator converts to scientific notation, e notation, engineering notation, standard form and word form formats.

To enter a number in scientific notation use a carat ^ to indicate the powers of 10. You can also enter numbers in e notation. Examples: 3.45 x 10^5 or 3.45e5.

Order of magnitude will also be identified for the calculated standard form. The order of magnitude when written in standard form, is the nth power of 10. For example, 3.4 x 10^5 has an order of magnitude of 5 since 10 is raised to the 5th power.

How to Convert a Number to Scientific Notation

The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.

1. Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.
2. Count how many places you moved the decimal point. This number is b.
3. If you moved the decimal to the left b is positive.
   If you moved the decimal to the right b is negative.
   If you did not need to move the decimal b = 0.
4. Write your scientific notation number as a x 10^b and read it as “a times 10 to the power of b.”
5. Remove trailing 0’s only if they were originally to the left of the decimal point.

Example: Convert 357,096 to Scientific Notation

• Move the decimal 5 places to the left to get 3.57096
• a = 3.57096
• We moved the decimal to the left so b is positive
• b = 5
• The number 357,096 converted to scientific notation is 3.57096 x 10^5

Example: Convert 0.005600 to Scientific Notation

• Move the decimal 3 places to the right and remove leading zeros to get 5.600
• a = 5.600
• We moved the decimal to the right so b is negative
• b = -3
• The number 0.005600 converted to scientific notation is 5.600 x 10^-3
• Note that we do not remove the trailing 0’s because they were originally to the right of the decimal and are therefore significant figures.

E notation is basically the same as scientific notation except that the letter e is substituted for “x 10^”.

Convert Scientific Notation to a Real Number

Multiply the decimal number by 10 raised to the power indicated.

3.456 x 10^4 = 3.456 x 10,000 = 34560

3.456 x 10^-4 = 3.456 x .0001 = 0.0003456