Basic Math

Question 1

what is 0.000000004 in scientific notation?

What is -35,000,000,000 ?

Answer 1

for decimals count all 0’s including the one before the decimal point.
for whole numbers count all digits after the the point where you plan to place the decimal

0. 00000004 has 9 0’s in total therefore 4 x 10^-9
   - 35,000,000,000 has 10 digits after the number 3

therefore -3.5 x 10^10

Question 2

list the scientific notation for the following

nano - 
micro - 
milli - 
centi - 
kilo - 
mega - 
giga -

Answer 2

nano - 10^-9

micro - 10^-6

milli - 10^-3

centi - 10^-2

kilo 10^3

mega = 10^6

10^9

Question 3

What is the following laws of exponents

product law
quotient law
power law
inverse law

Answer 3

b^p x b^q = b^(p+q)

b^p / b^q = b^(p-q)

(b^p)^q = b^(p x q)

b^-p = 1/b^p

notice the base must be the same for these laws to apply

Question 4

true or false, (a x b)^p = a^p x b^p

Answer 4

true, same applies for a quotient to power

(a/b)^p = a^p / b^p

Question 5

what are the terms in y = mx + b ?

Answer 5

y and x are whatever coordinates you put in

m is the slope (rise over run)

b is the y intercept of the curve

Question 6

what do the curves look like of the following…

x^2

1/x^2

Answer 6

only looking at quadrant one

x^2 is a parabola which curves to the right and up

1 / x^2 is curling down and to the right approaching the x axis.

Question 7

log (ab) = log(a) + log(b)

log (a/b) = log (a) - log (b)

log (a^2) = 2 log (a)

t or f?

Answer 7

all three are true log laws

Question 8

what is

1. the log of 1
2. the log of a fraction
3. log of a whole number

Answer 8

log of 1 is always 0
log of a fraction (0.000-0.999) is negative
log of a whole number is positive

Question 9

from the equation [H3O+] = m x 10^-n is it possible to predict the pH when given numbers to substitute?

Answer 9

yes. For [H3O+] = m x 10^-n the pH will be between (n-1) and n.

if m < 3 it is closer to n
if m > 3 it is closer to (n-1)

Question 10

If the pH is = n.m then…

[H3O+] = y x 10^ -(n+1)

m > 3 then y is closer to 1
m < 3 then y is closer to 9

what is the [H3O+] for a pH of 9.2?

Answer 10

[H+] = y x 10^ -(9+1)

m = 2 which is less than 3 therefore y is closer to 9

[H+] = 6/7 x 10^-10