Compare numbers written in scientific notation

Learning Objectives Identify the components of a number written in scientific notation. Compare numbers with different positive exponents in scientific notation. Compare numbers with the same exponent but different coefficients in scientific notation. Compare numbers with different negative exponents in scientific notation. Determine the greater or lesser of two numbers expressed in scientific notation, including cases with positive and negative exponents. Order a small set of numbers written in scientific notation from least to greatest or greatest to least. Have you ever wondered how scientists compare the size of a tiny virus to a giant planet? 🦠🪐 It's all about understanding how to compare numbers, especially when they're super big or super small! In this le...

TermDefinitionExample Scientific NotationA way to write very large or very small numbers using powers of 10. It's written as a product of two factors: a coefficient (a number between 1 and 10, not including 10) and a power of 10.$6.02 \times 10^{23}$ (Avogadro's number) Coefficient (or Mantissa)The first part of a number in scientific notation. It must be a number greater than or equal to 1 and less than 10.In $3.45 \times 10^6$, the coefficient is $3.45$. Exponent (or Power of 10)The second part of a number in scientific notation, which is 10 raised to a power. This power indicates how many places the decimal point was moved.In $3.45 \times 10^6$, the exponent is $6$. Positive ExponentAn exponent that is a positive number. It indicates a very large number (greater than 1). The...

Comparing Numbers with Different Exponents When comparing two numbers in scientific notation, first look at their exponents. The number with the larger exponent is the greater number. This rule applies regardless of the coefficients. A larger power of 10 means a larger 'order of magnitude', making it the dominant factor in comparison. Comparing Numbers with the Same Exponents If two numbers in scientific notation have the same exponent, then compare their coefficients. The number with the larger coefficient is the greater number. Once the 'order of magnitude' is the same (same exponent), the coefficient determines which number is larger, just like comparing regular decimal numbers. Comparing Positive and Negative Exponents Any number with a positive...