Deck 1: Numerical Computation

Question 1

Insert the proper sign of equality or inequality $(=, \approx,>,<)$ between the pair of numbers: $1 / 3$ ________ 0.333 .

Answer 1

" $\approx$ "

Question 2

Insert the proper sign of equality or inequality $(=, \approx,>,<)$ between the pair of numbers: -0.5_______ $-2 / 3$ .

Answer 2

">"

Question 3

Insert the proper sign of equality of inequality $(=, \approx,>,<)$ between the pair of numbers: 0.31_________ -0.313 .

Answer 3

">"

Question 4

Evaluate the expression: $|27-9|-|-11-6|$ .

Question 5

Evaluate the expression: $-|6-7|+|-3-4|$ .

Question 6

Evaluate the expression: $-|4+1|-|-4+1|$ .

Question 7

Evaluate the expression: $-|-3+1-5|+|3-1+5|$ .

Question 8

Round each number to two decimal places.
(a) 23.746
(b) 54.995001
(c) 94.355

Question 9

Round each number to two significant digits.
(a) 80.60
(b) 523.905
(c) 72.164

Question 10

Round each number to the nearest thousand.
(a) 657495
(b) 4500.1
(c) 3500

Question 11

Round each number to the nearest tenth.
(a) 16.299
(b) 12.450
(c) 0.001

Question 12

Determine the number of significant digits in each approximate number.
(a) 0.076
(b) 14200
(c) 5.089
(d) 0.540

Question 13

Determine the number of significant digits in each approximate number.
(a) 50.5
(b) 0.03
(c) 30.0
(d) 1000

Question 14

Combine these approximate numbers and round appropriately: $8235.4+98$

Question 15

Combine these approximate numbers and round appropriately: $696+15.2$

Question 16

Combine these approximate numbers and round appropriately: $-60.6-(-1.21)$

Question 17

An ocean liner sailed 715 nautical miles in one day and 689 in the next. How many nautical miles did the liner sail altogether?

Question 18

Maria has exactly $\$ 1500$ available for monthly expenses. She spent $\$ 479$ on transportation, $\$ 268$ on food, and $\$ 317$ for rent. Determine the amount remaining in her account.

Question 19

The changes in tide in the Bay of Fundy were measured at Parrsboro, Nova Scotia. At 6 a.m., the water level was $1.5 \mathrm{~m}$ . By $9 \mathrm{a} . \mathrm{m}$ . it had risen $6.3 \mathrm{~m}$ , and by noon it had risen another $4.6 \mathrm{~m}$ . The last measurement at 4 p.m. was $8.0 \mathrm{~m}$ lower than the noon level. What was the water level at 4 p.m.?

Question 20

Multiply these approximate numbers and keep the proper number of significant digits in your answer" $0.2001 \times 3.49$ "

Question 21

Multiply these approximate numbers and keep the proper number of significant digits in your answer" $5.300 \times(-8.72)$ "

Question 22

Multiply these approximate numbers and keep the proper number of significant digits in your answer" $67000 \times 23.54 \times 6.712$ "

Question 23

Two cars are exactly $1000 \mathrm{~km}$ apart. They have to meet each other within 9 hours. If they both start at the same time and one car drives at $90.3 \mathrm{~km} / \mathrm{h}$ and the other car at $88.7 \mathrm{~km} / \mathrm{h}$ , will they meet each other in time?

Question 24

If one tidal turbine in the Bay of Fundy can generate $4555 \mathrm{MWh}$ of electrical energy in one year, how much energy can 250 turbines generate in one year?

Question 25

Divide, and then round your answer to the proper number of digits: $-629.5 \div-89.34$

Question 26

Divide, and then round your answer to the proper number of digits: $-34825 \div 6592.3$

Question 27

A beverage company produces 15650 cans of pop monthly. How many 12 -can cartons can be completely filled and how many cans will be left over?

Question 28

Compute the reciprocal of the following number, keeping the appropriate number of digits in your answer "1503.0".

Question 29

Compute the reciprocal of the following number, keeping the appropriate number of digits in your answer is -12.5

Question 30

What volume of silver is needed to make a silver electrode weighing $155 \mathrm{~g}$ if the density of silver is $10.49 \mathrm{~g} / \mathrm{cm}^{3}$ ?

Question 31

If the slope of a tangent line at a point is $m$ , then the slope of the normal line at that point is $-k$ where $k$ is the reciprocal of $m$ . What is the slope of the normal line when the tangent line has slope -0.500 ?

Question 32

For capacitors wired in series, the equivalent capacitance is calculated using $\frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}$ . (See Eq. A72.) What is $C$ if $C_{1}=24$ microfarads $(\mu \mathrm{F})$ and $C_{2}=15 \mu \mathrm{F}$ ?

Question 33

The half-life of a chemical reaction, $t_{\frac{1}{2}}$ , is the time it takes for half of the original substance to react. For certain reactions, the half-life is found by the equation $t_{\frac{1}{2}}=\frac{1}{k C_{0}}$ seconds, where $k$ is a constant (different for each reaction) and $C_{0}$ is the original concentration of reactant. Find $t_{\frac{1}{2}}$ if $k=0.487$ and $C_{0}=1.201$ .

Question 34

Evaluate each power without using a calculator. Do not round your answers.
(a) $6^{2}$
(b) $(-1)^{70}$
(c) $10^{-2}$

Question 35

Evaluate each power without using a calculator.
(a) $1^{5}$
(b) $(-2)^{3}$
(c) $10^{-4}$

Question 36

Evaluate each expression, retaining the proper number of digits in your answer.
(a) $(4.25)^{-2}$
(b) $(53.8)^{2 / 5}$

Question 37

Evaluate each expression, retaining the proper number of digits in your answer.
(a) $(4.99)^{2}$
(b) $(14.05)^{-0.3500}$

Question 38

Evaluate each radical without using your calculator.
(a) $\sqrt[3]{8}$
(b) $\sqrt[3]{-27}$
(c) $\sqrt[4]{16}$

Question 39

Evaluate each radical, retaining the correct number of digits in your answer.
(a) $\sqrt{6.08}$
(b) $\sqrt[3]{0.056}$
(c) $\sqrt[5]{-6.301}$

Question 40

The moment of inertia of a solid sphere with mass $M$ and radius $R$ is $\frac{2 M R^{2}}{5}$ . Therefore, the moment of inertia of a sphere with a mass of $12.0 \mathrm{~kg}$ and a radius of $5.29 \mathrm{~m}$ is $(2 / 5)(12.0)(5.29)^{2} \mathrm{~kg} \cdot \mathrm{m}^{2}$ . Calculate this moment of inertia.

Question 41

The equilibrium constant $K_{c}$ for a chemical reaction $a A+b B \rightleftharpoons c C$ is given by $K_{c}=\frac{[C]^{c}}{[A]^{a}[B]^{b}}$ , where $[A]$ , $[B]$ , and $[C]$ are the equilibrium concentrations of $A, B$ , and $C$ . For the reaction $\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}$ , equilibrium concentrations were calculated to be $\left[\mathrm{H}_{2}\right]=0.0057,\left[\mathrm{I}_{2}\right]=0.0059$ , and $[\mathrm{HI}]=0.013$ . What is $K_{c}$ for this reaction?

Question 42

The Pythagorean Theorem says that the length of the hypotenuse is the root of the sum of the squares of the two legs. Therefore, the length of the hypotenuse of a right triangle with legs $178.2 \mathrm{~cm}$ and 78.4 $\mathrm{cm}$ long is $\sqrt{(178.2)^2+(78.4)^2}$ . Calculate this length.

Question 43

The radius of a sphere with volume $13.1 \mathrm{~m}^{3}$ is equal to $\sqrt[3]{\frac{3(13.1)}{4 \pi}}$ . Calculate this radius.

Question 44

Perform each computation, keeping the proper number of digits in your answer.
(a) $(24.5 \times 0.040)+(12.5 \times 0.13)$
(b) $\frac{7.26}{3.15}-\frac{4.902}{3.85}+\frac{9.27}{6.52}$
(c) $\frac{14.375+0.12}{32-12.11}$

Question 45

Perform each computation, keeping the proper number of digits in your answer.
(a) $(170+12.5 \times 11.1)-\sqrt{4.32}$
(b) $\frac{1.21}{(-3.5)(67.4)}+\frac{2.57}{(-9.27)(6.53)}$

Question 46

Perform each computation, keeping the proper number of digits in your answer.
(a) $\sqrt{86.334-49.251+0.703}$
(b) $\sqrt{74.8}-\sqrt[3]{9.01}+\sqrt[5]{-5.05}$
(c) $\left(\frac{5.6+7.24}{\sqrt{25.6}}\right)^{3}$

Question 47

Perform each computation, keeping the proper number of digits in your answer.
(a) $\sqrt{(20.954)(17.5)(67.34)}$
(b) $\sqrt{75}-\sqrt[5]{-35}-\sqrt[5]{35}$
(c) $\left(\frac{0.056-4.23}{\sqrt[3]{25.6}}\right)^{2}$

Question 48

Perform each computation, keeping the proper number of digits in your answer.
(a) $\frac{\sqrt{39}+56.1}{49.5}$
(b) $(2.1)^{3}-(3.9)^{5}$
(c) $\frac{14^{2}}{9.0^{2}+5.0}$

Question 49

For a simply-supported $4.0 \mathrm{~m}$ beam carrying a uniform load of $3.5 \mathrm{~N} / \mathrm{m}$ , the deflection at $x$ metres is given by $y=\frac{3.5}{24 k}\left(4.0^{3} x-8.0 x^{3}+x^{4}\right)$ , where $k$ is a constant. If $k=41000000$ , what is the deflection at $1.2 \mathrm{~m} ?$

Question 50

Write each number in scientific notation.
(a) 25000000
(b) $234 \times 10^{-5}$
(c) $0.034 \times 10^{3}$
(d) 0.0005690

Question 51

Write each number in engineering notation.
(a) 1320000
(b) $56 \times 10^{4}$
(c) $0.075 \times 10^{-5}$
(d) 0.002895

Question 52

Convert each number from scientific notation to decimal notation.
(a) $3.5 \times 10^{-5}$
(b) $1.205 \times 10^{3}$
(c) $5.0 \times 10^{-7}$
(d) $9.9 \times 10^{4}$

Question 53

Convert each number from scientific notation to decimal notation.
(a) $2.55 \times 10^{4}$
(b) $-3.4 \times 10^{-3}$
(c) $3.0 \times 10^{6}$
(d) $2.200 \times 10^{-1}$

Question 54

Convert each number from engineering notation to decimal notation.
(a) $2.67 \times 10^{6}$
(b) $92.1 \times 10^{-3}$
(c) $771 \times 10^{3}$
(d) $64.0 \times 10^{-9}$

Question 55

Combine without using a calculator. Write your answer in scientific notation: $\left(2.01 \times 10^{3}\right)+\left(3 \times 10^{2}\right)$

Question 56

Combine without using a calculator. Write your answer in scientific notation: $\left(6.42 \times 10^{-2}\right)-$ $\left(5 \times 10^{-4}\right)+\left(9 \times 10^{-3}\right)$

Question 57

Multiply and write your answer in scientific notation. Combine powers of ten by hand or with a calculator: $\left(8.61 \times 10^{10}\right)\left(4.35 \times 10^{-6}\right)$

Question 58

Divide and write your answer in scientific notation. Combine powers of ten by hand or with a calculator: $\left(1.42 \times 10^{-3}\right) \div\left(4.32 \times 10^{-4}\right)$

Question 59

Write this expression in scientific notation: $-2.425 \times 10^{-2 / 3}$

Question 60

Write this expression in engineering notation: $1266 \times 10^{2 / 5}$

Question 61

Write this expression in engineering notation: $14 \times 10^{-2.75}$

Question 62

The Earth has a mass of $5980000000000000000000000 \mathrm{~kg}$ . Write this mass in scientific notation.

Question 63

The charge on an electron is 0.00000000000000000016 coulombs. Write this charge in scientific notation.

Question 64

Tides are estimated to carry $2.4 \times 10^{6} \mathrm{~m}^{3}$ of sediment through the narrowest part of the Bay of Fundy every year. Write this volume in decimal notation.

Question 65

Convert the following imperial units.
(a) 3450 yards to miles
(b) 1.2 tons to pounds
(c) 3.55 feet to inches

Question 66

Convert the following metric units. Write your answer in scientific notation if the numerical value is greater than 1000 or less than 0.1 .
(a) $567000 \mathrm{~cm}$ to $\mathrm{km}$
(b) 74000 nanohms to deciohms
(c) $3.5 \times 10^{-6}$ giganewtons to millinewtons

Question 67

Convert the following metric units. Write your answer in scientific notation if the numerical value is greater than 1000 or less than 0.1 .
(a) $0.0053 \mathrm{~km}$ to $\mathrm{cm}$
(b) $3.50 \times 10^{-9}$ megafarads to picofarads
(c) 25000 microlitres to hectolitres

Question 68

Convert between units.
(a) 5.67 feet to metres
(b) 24.2 kilograms to pounds
(c) 3510 litres to U.S. gallons
(d) 0.4500 imperial gallons to cubic centimetres

Question 69

Convert between units.
(a) 48 centimetres to inches
(b) 0.85 ounces to grams
(c) 450 watts to horsepower
(d) 4.8 cubic metres to U.S. gallons

Question 70

Convert the following areas and volumes.
(a) 56 acres to square kilometres
(b) 250 square feet to square metres
(c) 12 cubic yards to cubic metres
(d) 1500 cubic centimetres to cubic feet

Question 71

Convert the following areas and volumes.
(a) 16 square centimetres to square feet
(b) 0.750 square metres to square inches
(c) 62.5 cubic metres to cubic yards
(d) 221 cubic feet to imperial gallons

Question 72

Convert units for the following time rates.
(a) 45.5 miles per hour to kilometres per hour
(b) 0.25 miles per hour to knots
(c) 7.5 metres per hour to feet per minute

Question 73

Convert units for the following unit prices.
(a) $\$ 45.99$ per kilogram to dollars per gram
(b) 34 cents per square metre to dollars per acre
(c) 25 cents per ounce to dollars per pound

Question 74

How many more metres will a car travel in $12 \mathrm{~min}$ at a speed of $50 \mathrm{~km} / \mathrm{h}$ than it will at a speed of $40 \mathrm{~km} / \mathrm{h}$ ?

Question 75

Jordan cycles $2 \mathrm{~km}$ in $15 \mathrm{~min}$ and Gaurav cycles $24 \mathrm{~km}$ in 2 hours. Who cycles faster?

Question 76

The Peak 2 Peak gondola in British Columbia joins Whistler and Blackcomb Mountains.
(a) The gondola cars travel at $7.5 \mathrm{~m} / \mathrm{s}$ . Convert this speed to $\mathrm{km} / \mathrm{h}$ .
(b) The longest unsupported span is $3.024 \mathrm{~km}$ . What is this span in miles?
(c) The highest point above the ground is $1427 \mathrm{ft}$ . What is this in metres?

Question 77

A copper nanowire has a cross-sectional area of $1600 \mathrm{~nm}^{2}$ . Use scientific notation to write the area in square inches.

Question 78

The latent heat of fusion for cherries is $115 \mathrm{Btu} / \mathrm{lb}$ . What is this in $\mathrm{kJ} / \mathrm{kg}$ ?

Question 79

Substitute $x=3$ into $y=4 x^{4}+2 x^{2}$ . Do not round your answer.

Question 80

Substitute $x=-2$ into $y=3 x^{2}+4 x^{2}$ . Do not round your answer.