Divide numbers written in scientific notation

Learning Objectives Recall and apply the quotient rule of exponents to powers of 10. Divide the coefficients of two numbers written in scientific notation. Combine the results of dividing coefficients and subtracting exponents to form a preliminary answer. Convert a non-standard result into proper scientific notation by adjusting the coefficient and exponent. Solve multi-step problems involving the division of numbers in scientific notation. Interpret and solve real-world problems that require dividing very large or very small numbers. The mass of the Earth is about 6 x 10^24 kg, and the mass of the Moon is about 7 x 10^22 kg. How many times more massive is the Earth than the Moon? 🌍🤔 This tutorial will teach you a powerful shortcut for dividing extremely large or small n...

TermDefinitionExample Scientific NotationA method for expressing very large or very small numbers as a product of a coefficient and a power of 10. The standard form is a × 10^n, where 1 ≤ |a| < 10 and n is an integer.The number 5,972,000,000,000,000,000,000,000 kg (mass of Earth) is written as 5.972 × 10^24 kg. CoefficientThe decimal number part of a number in scientific notation. It must be greater than or equal to 1 and less than 10.In the number 3.5 × 10^8, the coefficient is 3.5. BaseIn the context of scientific notation, the base is always 10.In the number 3.5 × 10^8, the base is 10. ExponentThe power to which the base 10 is raised. It indicates the magnitude and direction the decimal point was moved from standard form.In the number 3.5 × 10^8, the exponent is 8. Quotient Rule of...

Division Rule for Scientific Notation \frac{(a \times 10^n)}{(b \times 10^m)} = (\frac{a}{b}) \times 10^{(n - m)} To divide two numbers in scientific notation, first divide their coefficients. Then, divide their powers of 10 by subtracting the exponents. Quotient Rule of Exponents (for Base 10) \frac{10^n}{10^m} = 10^{n-m} This is the fundamental property of exponents that we use to handle the powers of 10 in our division problems. Remember to subtract the bottom exponent from the top one. Adjusting the Result (Normalization) If (a/b) is not between 1 and 10, adjust the decimal and the exponent to put the number in proper scientific notation. If your calculated coefficient is too small (e.g., 0.25) or too large (e.g., 25), you must move the decimal point and change t...