Compare numbers written in scientific notation

Learning Objectives Identify the coefficient and exponent in a number written in scientific notation. Compare two numbers in scientific notation by first examining their exponents. Compare two numbers in scientific notation with the same exponent by comparing their coefficients. Correctly order a set of numbers written in scientific notation from least to greatest or greatest to least. Explain the significance of positive and negative exponents when comparing numbers in scientific notation. Apply comparison techniques to solve simple real-world problems involving very large or very small numbers. Have you ever wondered how scientists compare the size of a galaxy to a planet, or the weight of an atom to a grain of sand? 🌌🔬 It's all about comparing numbers that are incr...

TermDefinitionExample Scientific NotationA way to write very large or very small numbers using powers of 10. It's written as a product of a coefficient (a number between 1 and 10, not including 10) and a power of 10.$6.02 \times 10^{23}$ (Avogadro's number) CoefficientThe first part of a number in scientific notation. It's a number greater than or equal to 1 and less than 10.In $3.45 \times 10^6$, the coefficient is $3.45$. ExponentThe small number written above and to the right of the base (which is always 10 in scientific notation). It tells you how many places to move the decimal point.In $3.45 \times 10^6$, the exponent is $6$. Positive ExponentAn exponent that is a positive number. It indicates a very large number (move the decimal to the right).$10^5 = 100,000$ Negati...

Rule 1: Comparing Exponents For two numbers $M \times 10^a$ and $N \times 10^b$, if $a > b$, then $M \times 10^a > N \times 10^b$. The number with the larger exponent (when comparing positive exponents, or when comparing a positive to a negative exponent) is the larger number. This is the first and most important step in comparison. Rule 2: Comparing Coefficients (Same Exponents) For two numbers $M \times 10^a$ and $N \times 10^a$, if $M > N$, then $M \times 10^a > N \times 10^a$. If the exponents are the same, compare the coefficients. The number with the larger coefficient is the larger number. Rule 3: Comparing Negative Exponents For two numbers $M \times 10^a$ and $N \times 10^b$ where $a$ and $b$ are negative, the number with the exponent closer to zer...