M3A2: How can we use scientific notation to work with large numbers? February 1st, 2017 Outcome: Be precise in simplifying integral exponents. 1. Write each number as a product of a decimal number between 1 and 10 and a power of 10. (a) 234, 000 (b) 3.331 (c) 532,100,000 (d) 0.0000000012 2. Perform the following operations without expressing the numbers in decimal notation. (a) (1.42 x 1015)(2.4 x 1013) !.!" × !!!!
(b) ! × !!!"
3. (a) Without performing the calculation, estimate which expression is larger. Explain how you know. !"
4×10
4×10!"
(2×10 ) and 2×10!!
!
(b) Now that you have estimated, perform the operations with the numbers in scientific notation. Explain why number is larger without converting them to decimal notation. A positive, finite decimal 𝑠 is said to be written in scientific notation if it is expressed as a product 𝑑×10! , where 𝑑 is a finite decimal number so that 1 ≤ 𝑑 < 10, and 𝑛 is an integer. The integer 𝑛 is called the order of magnitude of the decimal 𝑑 ×10! . 3
-­‐4
Example: 2,300 = 2.3 x 10 0.000567 = 5.67 x 10