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.
- 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.
- Count how many places you moved the decimal point. This number is b.
- 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. - Write your scientific notation number as a x 10^b and read it as “a times 10 to the power of b.”
- 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
