Define: Exponent Rule for dividing like bases applied to SN:
Define: What words tell you to divide:
Define: Why is “how many times larger” a division problem?
#1: (6.3 * 10^8)/(2.1 * 10^3) = ?
#2: (9.4 * 10^4)/(4.7 * 10^7) = ?
#3: In 2010, there were about 4 × 10^7 people living in California and about 1 × 10^6 people living in Rhode Island. How many times larger was the population of California than the population of Rhode Island?
#4: Pablo divided (6 x 10^8) by (2 x 10^-4), and got a final answer of 3 x 10^-2. Explain what mistake Pablo made, and give the correct solution.
#5: Write a division problem in which two numbers written in scientific notation have a quotient of 5 x 10^-5.
Exponent Rule for dividing like bases applied to SN: When dividing numbers in scientific notation with like bases, you subtract the exponents.
Words that tell you to divide: Words like divide, split, distribute, share, separate, etc.
"Why is 'how many times larger' a division problem?": When comparing two numbers to determine how many times larger one is than the other, you essentially have to divide one number by the other to find the ratio or multiplier.
#1: (6.3 * 10^8)/(2.1 * 10^3) = 3 * 10^5
#2: (9.4 * 10^4)/(4.7 * 10^7) = 2 * 10^-3
#3: California's population was 40 times larger than Rhode Island's population. (4 * 10^7)/(1 * 10^6) = 40
#4: Pablo's mistake was adding the exponents instead of subtracting them. The correct solution is (6 * 10^8) / (2 * 10^-4) = 3 * 10^12.
#5: (2 * 10^-4) / (4 * 10^-9) = 5 * 10^-5.