Scientific Notation
What is scientific notation?
A way to shorten long numbers
What is an exponent?
It indicates how many times the base is multiplied by itself
Which is incorrect:
7^2 = 49 or 7^2 = 14
7^2 = 49
a species of bacteria doubles every hour if there are 500 bacteria now how many will there be in 6 hours
N=500 x 2^6=500x64=32000
What does it mean to compare and order a exponent?
Take all of your numbers and order them least to greatest. For example: 6^2,7^2,4^8
How do you convert standard form?
Move the decimal until it's less than ten but more than one
How do you do base times exponent?
7^3 = 7 x 7 x 7 =343
Whats the law of exponents?
The laws of exponents, also known as rules of exponents, provide guidelines for simplifying expressions and calculations involving powers.
A grain of rice is placed on the first square of a chessboard, and the amount doubles on each square. How many grains are on the 10th square?
2^9=512
Which is greater: 3^2 or 2^3?
3^2(=9) is greater than 2^3 (=8)
What is the equation to convert standard form to scientific notation?
A x10^n
Convert this: 5^3 into standard form
5 x 5 x 5 = 125
Convert this: 3^12
531441
A cube has sides of length 323^232 cm. What is the volume of the cube?
729
Put least to greatest: 10^1, 2^4, and 3^3
3^3,2^4,10^1
Convert 0.0071 into scientific notation
7.1 x 10^-3
Why do you use exponents?
To simply equations like this one: 7x7x7x7x7x7x7x7= 5764801
What can you not do for exponents?
You can not distribute exponents over addition and subtraction
A grain of sand has a mass of 2.3×10−42.3 \times 10^{-4}2.3×10−4 grams. If you have 4.0×1064.0 \times 10^64.0×106 grains, what is the total mass?
=920 grams
Which one is smaller: 5^2 or 3^3
5^2=25 and 3^3=27 so 3^3 is greater
Convert 1.45 x 10^-4 into standard form
0.000145
simplify and solve: 6x6x6x6x6
6^5 = 7776
what do you get when you multiply x^3 X x^4
X^7
The distance from Earth to the sun is approximately 1.5×1081.5 \times 10^81.5×108 km. Light travels at 3.0×1053.0 \times 10^53.0×105 km/s. How many seconds does it take for sunlight to reach Earth?
500 seconds
Order least to greatest: 2^4,3^2, and 4^2
3^2, 2^4, 4^2