Work with radicals and integer exponents. NC.8.EE.3 Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times as much one is than the other. Clarification Checking for Understanding Students use their knowledge of the base ten number system and Write the following into scientific notation: exponents to rewrite numbers using scientific notation. Students a) The distance between the sun b) The distance between the sun interpret scientific notation generated when using technology. and the Earth is 93,000,000 and Neptune is 2,795,000,000 Students compare numbers written in scientific notation and express miles. miles. the multiplicative relationship between the numbers. c) A type of fairyfly is the smallest d) An average bacterium is about For example: Which of the following represents a larger known flying insect and is only 0.00004 inches long. number? 0.0059 inches long. a) 1.5 x 109 b) 7.5 x 10 Solution: 1.5x10* is the larger number For your answer, how many times larger is your answer then the Use the information from above to answer the following questions: smaller number? e) In astronomy, the distance between the sun and the Earth is known as 1 AU, or Solution: 1.5 x 10"is 20 times larger than 7.5 x 10' astronomical unit. Measured in AUs, what is the distance between the sun and Notice that 1.5 is .2 times 7.5. Looking at just the 105, 109is 100 times larger then 10. Neptune? (0.2)(100) = 20 f) If average sized bacteria were placed in a straight line, how many of bacteria Students should see more than just a division problem but should see would be needed to equal the length of the smallest known flying insect, a the multiplicative relationships that are unique to scientific notation. fairyfly