Dividing In Scientific Notation
Dividing numbers in scientific notation in Grade 8 Saxon Math Course 3 involves dividing the coefficients and subtracting the exponents of the powers of 10. Students then normalize the result to ensure the coefficient is between 1 and 10. This skill is used extensively in science for calculations involving extremely large or small quantities.
Key Concepts
Property To divide numbers in scientific notation, divide the coefficients and subtract the exponents. $\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m n}$.
Examples $\frac{9.6 \times 10^7}{3.0 \times 10^2} = \frac{9.6}{3.0} \times 10^{7 2} = 3.2 \times 10^5$ $\frac{3.0 \times 10^8}{4.0 \times 10^4} = 0.75 \times 10^4 = 7.5 \times 10^3$ $\frac{7.5 \times 10^6}{2.5 \times 10^6} = 3 \times 10^0 = 3$.
Explanation It's the reverse of multiplication! Divide the front numbers and subtract the exponents of the powers of 10. If your final coefficient is less than 1, you'll need to slide the decimal point and lower the exponent to get it back into the right format.
Common Questions
How do you divide numbers in scientific notation?
Divide the coefficients and subtract the exponent of the divisor from the exponent of the dividend. For example, (8 x 10^6) divided by (2 x 10^2) = 4 x 10^4.
What do you do if the result coefficient is not between 1 and 10?
Normalize the result by adjusting the decimal point in the coefficient and modifying the exponent accordingly to put the answer in proper scientific notation form.
Why do you subtract exponents when dividing scientific notation?
This follows the quotient rule for exponents: when dividing same-base numbers, subtract the exponents. Since both are powers of 10, dividing them gives 10 raised to the difference.
How do you divide scientific notation with negative exponents?
Apply the same rule: divide coefficients and subtract exponents, including negatives. For example, (6 x 10^-3) divided by (3 x 10^2) = 2 x 10^-5.
How is dividing in scientific notation used in Saxon Math Course 3?
Saxon Math Course 3 applies this skill in scientific contexts such as calculating speed from distance and time when values are expressed in scientific notation.