Scientific Notation Calculator and Converter

This free scientific notation calculator and converter can perform a range of operations in scientific notation, including adding, subtracting, multiplying, and dividing numbers. It can also convert real decimal numbers to scientific notation, and vice versa.

To use the scientific notation calculator, simply input the numbers in scientific notation, select an operation, and click on the "Calculate" button to generate the output.

What is Scientific Notation?

Scientific notion, which is also referred to as "Standard Form" or "Exponential Form", represents a numerical value that is recorded in the following form:

a × 10ⁿ (1 ≤ a < 10, n is an integer)

It can readily characterize both very large and very small numbers. Examples of scientific notation: 3,500,000 = 3.5 × 10⁶; 0.0000425 = 4.25 × 10^-5.

When scientific notation is applied, a large number is transformed into a corresponding decimal number that is between 1 and 10, multiplied by 10 raised to a given positive power, and small numbers are transformed into a corresponding decimal number between 1 and 10, multiplied by 10 raised to a given negative power.

Converting numbers into numeric form can be very beneficial in a range of disciplines including engineering, mathematics, and computing. In a calculator or computer, E or e, which stand for exponential, are employed to denote the power of 10.

E Notation

E notation, which is also referred to as exponential notation, is like scientific notation in that it involves multiplying a decimal number between 1 and 10 by 10 raised to a given power. When E notation is applied, the letter e or E replaces the "times 10 raised to a power" factor, and the number that follows the "e" is indicative of the number of powers of 10.

Scientific Notation Calculations - Addition, Subtraction, Multiplication, and Division

N₁ = a × 10ⁿ , N₂ = b × 10^m

N₁ and N₂ are numbers in scientific notation.

Addition and Subtraction

N₁ + N₂ = a × 10ⁿ + b × 10^m

Example 1: (3.12 × 10^-2) + (4.3 × 10^-3) = (3.12 × 10^-2) + (0.43 × 10^-2) = 3.55 × 10^-2

N₁ - N₂ = a × 10ⁿ - b × 10^m

Example 2: (6.35 × 10⁶) - (2.25 × 10⁴) = (6.35 × 10⁶) - (0.0225 × 10⁶) = 6.3275 × 10⁶

Multiplication

N₁ × N₂ = ab × 10^{n + m}

Example 3: (5.2 × 10²¹)(3.45 × 10⁴) = (5.2)(3.45) × 10⁽²¹⁺⁴⁾ = 17.94 × 10²⁵ = 1.794 × 10²⁶

Division

N₁ / N₂ = (a/b) × 10^{n - m}

Example 4: (8.1 × 10⁴)/(2.7 × 10^-6) = (8.1)/(2.7) × 10^{4 - (-6)} = 3 x 10¹⁰

Converting a number in Scientific Notation to Decimal Notation

Example A: Write the number 6.4 × 10⁷ in decimal notation.

6.4 × 10⁷ means 6.4×10×10×10×10×10×10×10

We multiply 6.4 by ten 7 times.

The decimal point is moved 7 places to the right.

6.4 × 10⁷ = 64,000

Example B: Write the number 5.82 × 10^-7 in decimal notation.

5.82 × 10^-7 means 5.82÷10÷10÷10÷10÷10÷10÷10

We divide 5.82 by ten 7 times.

The decimal point is moved 7 places to the left.

5.82 × 10^-7 = .000000582

Converting a number in Decimal Notation to Scientific Notation

Example C: Write 32,500,000 in scientific notation.

3.2500000

The decimal was moved 7 places to the left.

Therefore, the exponent is a +7

32,500,000 = 3.25 × 10⁷

Example D: Write .00000863 in scientific notation.

000008.63

The decimal was moved 6 places to the right.

Therefore, the exponent is a -6

.00000863 = 8.63 × 10^-6

You may also be interested in our Sig Fig Calculator (Significant Figures Calculator)