Application: Applying Exponent Rules to Scientific Notation
Application: Applying Exponent Rules to Scientific Notation is a Grade 7 math skill in Reveal Math Accelerated, Unit 13: Irrational Numbers, Exponents, and Scientific Notation, where students use the product and quotient of powers rules to multiply and divide numbers in scientific notation, maintaining proper format by keeping coefficients between 1 and 10. This skill is essential for science calculations involving very large or very small quantities.
Key Concepts
Property To raise a number in scientific notation to a power, apply the Power of a Product and Power of a Power properties. Raise the coefficient to the power, and multiply the exponents on the base 10: $$(a \times 10^n)^m = a^m \times 10^{n \cdot m}$$.
Examples Evaluating a Power in Scientific Notation: $$(2 \times 10^4)^3 = 2^3 \times (10^4)^3 = 8 \times 10^{12}$$ Adjusting to Proper Scientific Notation: $$(5 \times 10^{ 3})^2 = 5^2 \times (10^{ 3})^2 = 25 \times 10^{ 6}$$ Since 25 is greater than 10, adjust the decimal: $2.5 \times 10^{ 5}$. Applying to a Real World Formula (Volume of a Sphere): Find the volume $V = \frac{4}{3}\pi r^3$ for a sphere with radius $r = 3 \times 10^{ 2}$. $$V = \frac{4}{3}\pi (3 \times 10^{ 2})^3$$ $$V = \frac{4}{3}\pi (3^3 \times 10^{ 6})$$ $$V = \frac{4}{3}\pi (27 \times 10^{ 6}) = 36\pi \times 10^{ 6}$$.
Explanation When raising a number in scientific notation to a power, you are distributing that outside exponent to both the regular number (the coefficient) and the power of 10. This technique is incredibly useful for evaluating real world geometry or physics formulas—like calculating the volume of a microscopic sphere or a massive planet—without having to write out dozens of zeros!
Common Questions
How do you multiply numbers in scientific notation?
Multiply the coefficients together and add the exponents of the powers of 10. If the resulting coefficient is not between 1 and 10, adjust it and update the exponent accordingly.
How do you divide numbers in scientific notation?
Divide the coefficients and subtract the exponent of the divisor from the exponent of the dividend. Adjust the result to proper scientific notation if needed.
What exponent rule is used when multiplying powers of 10?
The product of powers rule: when multiplying two powers with the same base, add the exponents. So 10^3 x 10^4 = 10^(3+4) = 10^7.
What is Reveal Math Accelerated Unit 13 about?
Unit 13 covers Irrational Numbers, Exponents, and Scientific Notation, including exponent rules, converting between standard and scientific notation, and performing operations with scientific notation.