#### • Class 11 Physics Demo

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#### • 4501 scientific notation

Question:what are these numbers scientific notation 56,000 70,000 20,000 Now, assume each number for task 1 doubles. Show how each number is multiplied by 2 and find the new numbers. Be sure each number is in scientific notation!

Answers:In scientific notation you write a number with a long string of zeros in a shorthand fashion. 56000 Look at the first non-zero part and rewrite as a number between 1 and 10 56 -> 5.6 Compare where the decimal is now (after the 5) and where it was originally (4 places to the right or positive 4). This tells you the power of 10 to use. 56000 = 5.6x10^4 or 5.6E4 in calculator speak. The others work the same 70000 = 7.0x10^4 = 7.0E4 20000 = 2.0x10^4 = 2.0E4 What happens if you double a number in scientific notation? 2x(5.6x10^4) = 11.2x10^4, but this breaks the rule about the significant part being between 1 and 10. 11.2 = 1.12x10 11.2x10^4 = 1.12x10x10^4 = 1.12x10^5 or 1.12E5 Or 2x56000 = 112000 = 1.12x10^5 (because the decimal should be 5 to the right from its new location) 2x70000 = 140000 = 1.4x10^5 2x20000 = 40000 = 4.0x10^4 (Notice the power of ten doesn't change here.) Just in passing... .00000645 = 6.45x10^-6 = 6.45E-6 because the decimal belongs 6 steps to the left of its new location.

Question:1. Write the following value in scientific notation. 23,000,000 - 2.3 x 106 - 2.3 x 107 - 2.3 x 10-5 - 2.3 x 102 2. Write the following value in scientific notation. 7,400,000 - 7.4 x 106 - 7.4 x 107 - 7.4 x 10-5 - 7.4 x 102 3. Write the following value in scientific notation. 0.00000021 - 2.1 x 106 - 2.1 x 10-6 - 2.1 x 105 - 2.1 x 10-7 4. Write the following value in scientific notation. 0.00003165 - 3.165 x 106 - 3.165 x 10-6 - 3.165 x 10-5 - 3.165 x 108 5. Which value below is not equivalent to the others? - 7.27 x 101 - 72.7 - 727 x 100 - 7.27 x 10 6.Anything raised to the zero power will equal 1. True False 7. Write the following value in standard notation. 4.25 x 106 - 425,000 - 4,250,000 - 425,610 - 425,000,000 8. Write the following value in standard notation. 3.89 x 104 - 389,000 - 38,900,000 - 389,410 - 38,900

Answers:1. 2.3 x 10^7 2. 7.4 x 10^6 3. 2.1 x 10^-7 4. 3.165 x 10-5 5. 727 x 100 6. True 7. 4,250,000 8. 38,900 ____________ When changing to scientific notation, count the number of places the decimal point moves. When changing to scientific notation - Left is positive - Right is negative When changing from scientific notation - Left is negative - Right is positive

Question:how do you add and subtract in scientific notation ? example: 6.23 x 10 to the 6th power + 5.34 x 10 to the 6th power &how do you multiply and divide in scientific notation? example: (4.8x10 to the 5th power)x(2.0x10 to the 3rd power) example: (8.4x10 to the 6th)divided by(2.4x10 to the -3)

Answers:how do you add and subtract in scientific notation ? adjudst the to have the same exponent , then subtract: example: 6.23 x 10 to the 5th power + 1.23 x 10 to the 6th power becomes 6.23 x 10 to the 5th power + 12.3 x 10 to the 5th power = 18.53 X 10 to the 5th ================================= &how do you multiply multiply the numbers, add exponents: example: (4.8x10 to the 5th power)x(2.0x10 to the 3rd power) = 9.6 e8 ====================================== and divide in scientific notation? divide the numbers , subtract exponents: example: (4.8x10 to the 5th power)x(2.0x10 to the 3rd power) = 2.4 e 2 example: (8.4x10 to the 6th)divided by(2.4x10 to the -3) = 3.5 e9 (exp of 6) - (exp of -3) = 6 + 3 = exp of 9

Question:how do you figure out what the exponent should be after the ten for addition, subtraction, multiplication, and division. problems... addition-- (3.95 x 105) + (7.8 x 103) Subtraction-- (7.83 x 10-2) - (2.20 x 10-3) Multiplication-- (6.423 x 101) + (5.001 x 10-1) Division-- divide (9.2 x 10-3) by (6.3 x 106)

Answers:When multiplying exponents, you add them. Example: 10^5 x 10^3 = 10^8