Convert between standard and scientific notation

Learning Objectives Define scientific notation and identify its components (coefficient, base, exponent). Convert large numbers (greater than 10) from standard form to scientific notation. Convert small numbers (between 0 and 1) from standard form to scientific notation. Convert numbers from scientific notation with a positive exponent into standard form. Convert numbers from scientific notation with a negative exponent into standard form. Evaluate whether a number is written in proper scientific notation. Explain the relationship between the exponent's sign and the magnitude of the number. How far is it to the nearest star, Proxima Centauri? It's about 40,208,000,000,000 km away! 🔭 There has to be an easier way to write that. This lesson will teach you how to...

TermDefinitionExample Standard NotationThe typical, everyday way of writing numbers using digits.1,500,000 or 0.0025 Scientific NotationA method of writing numbers as a product of two parts: a coefficient and a power of 10.1.5 \times 10^6 or 2.5 \times 10^{-3} CoefficientThe first part of a number in scientific notation. It must be a number greater than or equal to 1 and less than 10 (1 ≤ |a| < 10).In 8.4 \times 10^5, the coefficient is 8.4. BaseThe number that is raised to a power. In scientific notation, the base is always 10.In 8.4 \times 10^5, the base is 10. ExponentThe power to which the base 10 is raised. It tells you how many places the decimal point was moved.In 8.4 \times 10^5, the exponent is 5. Positive ExponentIndicates a large number (a number greater than or equal to 10)...

Standard to Scientific Notation N = a \times 10^n To convert a number N into scientific notation, move the decimal point to create a coefficient 'a' where 1 ≤ |a| < 10. The number of places you moved the decimal is the exponent 'n'. If you moved the decimal left (for a large number), 'n' is positive. If you moved it right (for a small number), 'n' is negative. Scientific to Standard Notation (Positive Exponent) For a \times 10^n, where n > 0 Move the decimal point in the coefficient 'a' to the right 'n' places. Add placeholder zeros as needed. This will result in a large number. Scientific to Standard Notation (Negative Exponent) For a \times 10^{-n}, where n > 0 Move the decimal point in the coeffi...