Writing out a number like 602,000,000,000,000,000,000,000 in full is impractical — that's Avogadro's number, and scientists use it constantly. Scientific notation exists specifically to make numbers like this manageable.
A number in scientific notation is written as a value between 1 and 10, multiplied by a power of 10. For example, 602,000,000,000,000,000,000,000 becomes 6.02 × 10²³. The exponent tells you how many places the decimal point moved.
To convert a large number into scientific notation, move the decimal point left until only one non-zero digit remains before it, then count how many places you moved — that count becomes the positive exponent. For example, 45,000 becomes 4.5 × 10⁴.
For numbers smaller than 1, the process is similar but the exponent is negative. For example, 0.00032 becomes 3.2 × 10⁻⁴, since the decimal point moved four places to the right.
Most scientific calculators display very large or very small results automatically in scientific notation, often shown with an "E" or "×10" in the display — for example, 6.02E23 means 6.02 × 10²³.
To multiply two numbers in scientific notation, multiply the decimal parts together and add the exponents: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷. To divide, divide the decimal parts and subtract the exponents: (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴. This is significantly faster than multiplying or dividing the full expanded numbers directly, especially when the numbers involved have many digits.
Unlike multiplication, addition and subtraction in scientific notation require the exponents to match first. To add 3 × 10⁵ and 2 × 10⁴, first rewrite 2 × 10⁴ as 0.2 × 10⁵, then add the decimal parts: 3.2 × 10⁵. Students who skip this step and simply add the decimal parts directly (getting 5 × 10⁵ or 5 × 10⁴) end up with an answer that's off by a factor of 10.
Why does a negative exponent make a number smaller instead of negative?
Because a negative exponent means dividing by that power of 10 rather than multiplying — 10⁻⁴ literally means 1/10⁴, which is a small fraction (0.0001), not a negative quantity.
How do I know how many significant figures to keep in scientific notation?
Keep as many digits as your original measurement or calculation supports — scientific notation doesn't add or remove precision on its own, it just changes how the same value is displayed.
Calvo's scientific calculator automatically switches to scientific notation for very large or very small results, so you can see the conversion happen in real time, and cross-check your own manual conversions against the calculator's output while you practice.