Scientific Notation
Convert between standard and scientific notation
Standard to Scientific
Scientific to Standard
Common Scientific Values
Scientific Notation Guide
What is Scientific Notation?
A way to express very large or very small numbers as a coefficient (1-10) multiplied by a power of 10. Example: 5,000,000 = 5 × 10⁶
Converting to Scientific
Move the decimal point until you have a number between 1 and 10. Count the moves: right moves = negative exponent, left moves = positive exponent.
Multiplying & Dividing
Multiply/divide coefficients, then add/subtract exponents. (2×10³) × (3×10⁴) = 6×10⁷
Frequently Asked Questions
How do you convert a large number to scientific notation?
Move the decimal point left until the number is between 1 and 10, counting each move as one power of 10. For 123,456,789: move the decimal 8 places left to get 1.23456789, giving 1.23456789 × 10⁸. Moving right (for small numbers) gives a negative exponent; 0.00045 = 4.5 × 10⁻⁴.
What is engineering notation and how does it differ from scientific notation?
Engineering notation is a variant of scientific notation where the exponent is always a multiple of 3 (matching SI prefixes like kilo, mega, giga). For 123,456,789: engineering notation is 123.456789 × 10⁶ instead of 1.23456789 × 10⁸. This aligns with real-world units like MHz and km.
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. If the resulting coefficient is not between 1 and 10, adjust: (5 × 10⁶) × (3 × 10⁴) = 15 × 10¹⁰ = 1.5 × 10¹¹. Division works similarly: divide coefficients and subtract exponents.
What does significant figures mean in scientific notation?
Significant figures are the meaningful digits in a measurement. In 1.23 × 10⁵, there are 3 significant figures. Scientific notation makes sig-fig counting straightforward — all digits in the coefficient are significant. The calculator counts and displays significant figures for each input.
What is Avogadro's number and why is scientific notation essential for it?
Avogadro’s number ≈ 6.022 × 10²³ is the number of atoms or molecules in one mole of a substance. Written in standard form it would be 602,200,000,000,000,000,000,000 — 24 digits. Scientific notation makes such constants readable and manageable in calculations, especially when multiplying or dividing them.