Question 1

When multiplying two numbers in scientific notation, such as $$ (A 	imes 10^x) 	imes (B 	imes 10^y) $$, what is the correct procedure?

Accepted Answer

Multiply the coefficients and add the exponents.

Question 2

What is the result of $$ (2.134 	imes 10^7$) 	imes (1.60 	imes 10^3$) 	imes (3.07 	imes 10^4$)  in $$proper scientific notation?

Accepted Answer

$$1.05 	imes 10$$^{15}$$

Question 3

When dividing two numbers in scientific notation, such as $$ \frac{A 	imes 10^x}{B 	imes 10^y} $$, what is the correct procedure?

Accepted Answer

Divide the coefficients and subtract the exponents.

Question 4

Calculate $$ \frac{7.33 	imes 10^9$ 	imes 9.89 	imes 10^3$}{6.12 	imes 10^7$} $$ and express your answer in scientific notation.

Accepted Answer

$$1.19 	imes 10^6$

Question 5

When adding or subtracting numbers in scientific notation, what must be true about the exponents?

Accepted Answer

The exponents must be the same.

Question 6

What is the result of $$8.17 	imes 10^4$ + 1.25 	imes 10^4$?

Accepted Answer

$$9.42 	imes 10^4$

Question 7

Evaluate $$9.08 	imes 10$$^{-12}$$ - 1.17 	imes 10$$^{-12}$$ - 3.35 	imes 10$$^{-13}$$ and express your answer in scientific notation.

Accepted Answer

$$7.58 	imes 10$$^{-12}$$

Question 8

When raising a number in scientific notation to a power, such as $$ (3.0 	imes 10$$^{-3}$$)^2$$ $, what is the correct procedure?

Accepted Answer

Raise the coefficient to the power and multiply the exponent by the power.

Question 9

Calculate $$ (3.0 	imes 10$$^{-3}$$)^2$$ $.

Accepted Answer

$$9.0 	imes 10$$^{-6}$$

Question 10

What is the value of $$ \sqrt{6.0 	imes 10^9$} $$?

Accepted Answer

$$7.75 	imes 10^4$

Question 11

What is the value of $$ \log(1.0 	imes 10$$^{-7}$$) $$?

Accepted Answer

$$-7$$

Question 12

Which of the following is the correct value for $$ \log(0.0001) $$?

Accepted Answer

$$-4$$

Question 13

The Henderson-Hasselbalch equation is $$ \mathrm{pH} = \mathrm{p}K_a + \log \left( \frac{	ext{conjugate base}}{	ext{weak acid}} ight) . If$$ $$\mathrm{pH} = 4.83$$ and $$\mathrm{p}K_a = 3.83$$, what is the ratio of conjugate base to weak acid?

Accepted Answer

$$10$$

Question 14

Which of the following is the correct relationship for logarithms when multiplying two numbers $$a$$ and $$b$$?

Accepted Answer

$$\log(a \cdot b) = \log a + \log b$$

Question 15

Given $$\log 2 = 0.30$$ and $$\log 3 = 0.48$$, what is the value of $$\log 12$$?

Accepted Answer

$$1.08$$

Question 16

What is the value of $$\ln(2.13 	imes 10$$^{-1}$$) + \ln(2.3) + \ln(1.25)$$?

Accepted Answer

$$0$$

Question 17

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 18

If $$\log x = y$$, what is the value of $$x in $$terms of $$y$$?

Accepted Answer

$$x = 10^y$$

Question 19

Which of the following is the correct relationship for natural logarithms when dividing two numbers $$a$$ and $$b$$?

Accepted Answer

$$\ln \left( \frac{a}{b} \right) = \ln a - \ln b$$

Question 20

A chemist needs to calculate the pH of a buffer solution using the Henderson-Hasselbalch equation. If the concentration of the conjugate base is doubled while the weak acid remains constant, how does the pH change?

Accepted Answer

The pH increases by $$\log 2 ($$approximately 0.30).

Mathematical Operations and Functions in Introductory Chemistry

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