Scientific Notation Converter

What Is Scientific Notation?

Scientific notation is a way to express very large or very small numbers concisely. Any number is written as:

$$a \times 10^n$$

where 1 ≤ |a| < 10 (the coefficient) and n is an integer (the exponent or power of 10).

For example:

• The speed of light: 300,000,000 m/s = 3.0 × 10⁸ m/s
• The mass of a proton: 0.0000000000000000000000000016726 kg = 1.6726 × 10⁻²⁷ kg

How to Convert to Scientific Notation

To convert a number like 4,500,000 to scientific notation:

1. Move the decimal point left until you have a number between 1 and 10: 4.5
2. Count how many places you moved the decimal: 6 places to the left
3. Write as: $4.5 \times 10^6$

For a small number like 0.0072:

1. Move the decimal right until you have a number between 1 and 10: 7.2
2. Count the places moved: 3 places to the right → negative exponent
3. Write as: $7.2 \times 10^{-3}$

Multiplying and Dividing in Scientific Notation

One of the biggest advantages of scientific notation is that multiplication and division are easy:

• Multiply: Multiply the coefficients and add the exponents: $(a \times 10^m)(b \times 10^n) = ab \times 10^{m+n}$
• Divide: Divide the coefficients and subtract the exponents: $\dfrac{a \times 10^m}{b \times 10^n} = \dfrac{a}{b} \times 10^{m-n}$

After performing the operation, adjust if the coefficient falls outside the 1–10 range. For example, $15 \times 10^4$ should be re-expressed as $1.5 \times 10^5$.

For rounding answers to the correct number of significant figures, use the significant figures calculator.

Frequently Asked Questions

What does E notation mean (e.g., 3.4E-5)?

The letter E (or e) is used in calculators and programming languages to represent "times 10 to the power of." So 3.4E-5 means $3.4 \times 10^{-5}$, which equals 0.000034.

Can the coefficient be negative?

Yes. A negative number like −0.0072 is written as $-7.2 \times 10^{-3}$. The negative sign applies to the entire number, not the exponent.

How is scientific notation used in real life?

Scientific notation is used heavily in physics, chemistry, astronomy, and engineering whenever extremely large or small numbers arise. Examples include distances in space (light-years), the sizes of atoms and molecules, national debt figures, populations of bacteria, and computer memory (bytes per storage device).