Compare numbers written in scientific notation

Learning Objectives Compare two numbers written in scientific notation by first analyzing their exponents. Compare two numbers written in scientific notation by analyzing their coefficients when the exponents are equal. Correctly use inequality symbols (<, >, =) to express the relationship between two numbers in scientific notation. Order a list of three or more numbers written in scientific notation from least to greatest or greatest to least. Explain how the exponent determines the order of magnitude and is the primary factor in a number's size. Apply the comparison of numbers in scientific notation to solve real-world problems involving large and small quantities. Which is heavier: a single star with a mass of 2.1 x 10³⁰ kg or all the ants on Earth with a combi...

TermDefinitionExample Scientific NotationA way of writing very large or very small numbers as a product of a coefficient and a power of 10. The general form is a × 10ⁿ.The number 5,800,000 is written as 5.8 × 10⁶ in scientific notation. CoefficientThe decimal number part in scientific notation. It must be greater than or equal to 1 and less than 10 (1 ≤ a < 10).In 7.34 × 10⁵, the coefficient is 7.34. ExponentThe power to which 10 is raised. It indicates the magnitude and direction the decimal point was moved from standard form.In 7.34 × 10⁵, the exponent is 5. In 2.1 × 10⁻⁴, the exponent is -4. Order of MagnitudeThe power of 10 that represents the general size of a number. It is determined by the exponent in scientific notation.A number like 5 × 10⁸ is one order of magnitude larger tha...

Rule 1: Comparing Exponents Given two numbers a × 10ⁿ and b × 10ᵐ, if n > m, then a × 10ⁿ > b × 10ᵐ. Always compare the exponents first. The number with the larger exponent is the greater number, regardless of the coefficients. Rule 2: Comparing Coefficients Given two numbers a × 10ⁿ and b × 10ⁿ, if a > b, then a × 10ⁿ > b × 10ⁿ. If and only if the exponents are the same, you then compare the coefficients. The number with the larger coefficient is the greater number.