When 605,000 is written in scientific notation, what will be the value of the decimal number?

The scientific notation calculator will take any decimal value and convert it to scientific notation. Here we will not only tell you what scientific notation is all about but also explain the scientific notation rules and discuss slight variations that might appear in different domains where people use scientific notation.

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How to Convert a Number to Scientific Notation
Example: Convert 357,096 to Scientific Notation
Example: Convert 0.005600 to Scientific Notation
Convert Scientific Notation to a Real Number
Additional Resources

Scientific notation is generally used with very large or very small numbers in applications such as physics, engineering, and chemistry. It condenses the numbers into a number a between 1 (included) and 10 (excluded) multiplied by 10 raised to an exponent, denoted as a × 10ⁿ.

When converting a number into scientific notation, we must remember a few rules. First, the decimal must be between the first two non-zero numbers. The number prior to the multiplication symbol is known as the significant or mantissa. The numbers of digits in the significant depends on the application and are known as significant figures. The significant figures calculator can assist in this situation. The value of the exponent depends on whether or not the decimal place is moved to the right or left to return to the original number. An example on how to convert a number into scientific notation is done in the next section.

To better understand these rules of scientific notation, let's discuss an example.

Suppose we want to convert 0.00345 to scientific notation:

Place the decimal between the first two non-zero numbers, so we have 3.45.
Count the number of decimal places that were moved, which in this case is 3.
Determine whether the decimal point must be moved to the left or right to return to the original number.
If the decimal is moved right, the exponent is negative. If the decimal is moved left, the exponent is positive.
Write in terms of a × 10ⁿ, in this case, 3.45 × 10⁻³.

Verify this result with our scientific notation calculator! If you wanted the answer to have two significant figures, you would have to round the significant to 3.5. The rounding calculator is a great tool to accomplish this task. Also helpful in converting numbers to scientific notation is the exponent calculator.

It's very easy to use Omni's scientific notation calculator: just input a number and our converter will do the rest.

Note that this scientific notation converter uses e plus or minus the exponent, instead of 10 raised to the exponent. There are several different notations used, depending on the application. Computer languages, engineering, and mathematical applications use similar but different ways to represent scientific notation.

If you are searching for useful maths calculators do not hesitate to take a look at the cube root calculator which enables you to calculate not only cube root but also roots of any degree.

Suppose you have two numbers written in scientific notation: a × 10ⁿ and b × 10ᵐ.

To multiply them, multiply the coefficients and add the exponents: (a×b) × 10ⁿ⁺ᵐ.
To divide the first one by the second, divide the coefficients and subtract the exponents: (a/b) × 10ⁿ⁻ᵐ.
The result need not be in scientific notation! It's recommended you verify if it is and perform the conversion if needed. You may use Omni's scientific notation calculator to do this task quickly and easily.

4.5×10³ or, equivalently, 4.5e3. This is because we want to write 4,500 as a × 10ⁿ with a ∈ [1,10) and n an integer.

5.7×10⁻⁴ or, equivalently, 5.7e-4. In this way, we've written our number as a × 10ⁿ with a ∈ [1,10) and n an integer.

Since the decimal place is between the leading nonzero digit and the adjacent digit on the right, there is no need to shift the decimal point. Therefore, 1.07 in scientific notation is: 1.07 * 100

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^".