Comparing Numbers in Scientific Notation
Comparing Numbers in Scientific Notation is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 10: Exponents and Scientific Notation, where students compare numbers expressed in scientific notation by first comparing the powers of 10 (a higher exponent means a larger number, assuming positive exponent) and then, if powers are equal, comparing the coefficients. This skill is critical for comparing very large or very small quantities in science and engineering.
Key Concepts
To compare numbers in scientific notation $a \times 10^n$ and $b \times 10^m$: 1. If $n m$, then $a \times 10^n b \times 10^m$ 2. If $n < m$, then $a \times 10^n < b \times 10^m$ 3. If $n = m$, compare the factors: if $a b$, then $a \times 10^n b \times 10^n$.
Common Questions
How do you compare two numbers in scientific notation?
First compare the powers of 10. The number with the larger exponent is greater. If the exponents are equal, compare the coefficients; the larger coefficient gives the larger number.
Which is greater: 4.2 x 10^8 or 9.1 x 10^7?
4.2 x 10^8 is greater. The exponent 8 is larger than 7, so 10^8 > 10^7, making 4.2 x 10^8 = 420,000,000 larger than 9.1 x 10^7 = 91,000,000.
How do negative exponents affect comparisons?
Numbers with negative exponents are very small (less than 1). A number with a more negative exponent is smaller. For example, 3 x 10^-6 < 8 x 10^-4 because -6 < -4.
What is Big Ideas Math Advanced 2 Chapter 10 about?
Chapter 10 covers Exponents and Scientific Notation, including exponent rules, writing numbers in scientific notation, and performing and comparing operations with scientific notation.