3 Vocabulary Terms - Define/Illustrate
Adding/Subtracting Fractions - we need a _______________
Adding/Subtracting expressions - we need
______________
Adding/Subtracting in SN - we need
______________
5 Problems - SHOW ALL WORK!
In 2012, the population of NY was about 2.4 x 10^7 and the population of Oregon was 4x10^5. What is the total population of the two states?
3.71 x 10^5 + 4.65 x 10^5
7.35 x 10^-7 + 2.16 x 10^-8
5 x 10^3 + 3 x 10^5 =
In 2006, the US had a Gross Domestic Product (GDP) of 1.313 x 10^13. The United Kingdom had a GDP of 1.93 x 10^12. What
were the combined GDPs of the US and the UK in 2006?
Incorrect Work/ Laila’s Solution Identify and Explain the error
(1.313 x 10^13) + (1.93 x 10^12)
1.313 + 1.93 = 3.243
10^13 + 10^12 = 10^25
The combined GDPs of the US and the UK in 2006 was
3.243 x 10^25.
What do I need help with?
Adding/Subtracting Fractions - we need a common denominator
Adding/Subtracting expressions - we need like terms
Adding/Subtracting in SN - we need to keep the same exponent
1. Total population of NY and Oregon: (2.4 x 10^7) + (4 x 10^5) = 2.4 x 10^7 + 0.4 x 10^7 = 2.8 x 10^7
2. 3.71 x 10^5 + 4.65 x 10^5 = 8.36 x 10^5
3. 7.35 x 10^-7 + 2.16 x 10^-8 = 7.35 x 10^-7 + 0.0216 x 10^-7 = 7.3716 x 10^-7
4. 5 x 10^3 + 3 x 10^5 = 5 x 10^3 + 300 x 10^3 = 305 x 10^3 = 3.05 x 10^5
5. Combined GDPs of US and UK: (1.313 x 10^13) + (1.93 x 10^12) = 1.313 x 10^13 + 0.193 x 10^13 = 1.506 x 10^13
Explanation: In the incorrect solution, Laila added the coefficients (1.313 + 1.93) correctly, but she added the exponents (10^13 + 10^12) incorrectly. The correct way to add exponents when multiplying or dividing numbers in scientific notation is to keep the exponent the same and operate on the coefficients. So the correct answer should be 1.506 x 10^13, not 3.243 x 10^25.