Scientific Notation

Practice Quiz

Put the following in order from smallest to largest.

•1.8x10-5

•8.7x1024

•0.7x10-3

•1.4x1040

Answers

Smallest Largest1.8x10-5 0.7x10-3 8.7x1024 1.4x1040

Scientists (and those studying science)

frequently must deal with numbers that are very

large or very small.

Instead of wasting time by writing many zeros before

and after numbers, a method of writing very large and very small numbers was invented.

It is called scientific notation.

Rules1) The first figure is a number from 1 to 9.

2) The first figure is followed by a decimal point and then the rest of the figures.

3) Then multiply by the appropriate power of 10.

Are these numbers written in scientific notation?

•60.5x105

•6.05x106

•0.65x100.65x10-2-2

•4.254.2522

Examples

•425=4.25x102 (102 is the same as 100, so you are really multiplying 4.25 by 100)

•0.00098=9.8x10-4 (10-4 is the same as 1/1000, so you are really multiplying 9.8 by 1/1000)

PracticeWrite the following in scientific notation:

•36000•0.0135•3951•0.632•0.00000090

Answers

•3.6x104

•1.35x10-2

•3.951x103

•6.32x10-1

•9.0x10-7

Math is easy-use your calculator!!!•4.2x104kg + 7.9x103kg=•5.23x106mm x 7.1x10-

2mm=•5.44x107g/8.1x104mol=

Answers

•4.99x104 kg•3.71x105mm2

•6.72x102 g/mol

Significant Figures

Rules• All non zero digits are significant

Ex: 127• Zeros between significant digits are always

significant (sandwich zeros) Ex: 106 • Leading zeros are never significant (placeholder

zeros)Ex: 0.005

• Trailing zeros are significant only if there is a decimal in the number

Ex: 25.30

Copy the examples below and write the number of significant figures1. 76231425162. 70843. 0.007614. 421.005. 0.5386. 50007. 5x103

8. 5.0 x103

9. 5000.10. 5120

Copy the examples below and write the number of significant figures1. 7623142516 (10)2. 7084 (4)3. 0.00761 (3)4. 421.00 (5)5. 0.538 (3)6. 5000 (1)7. 5x103 (1)8. 5.0 x103 (2)9. 5000. (4)10. 5120 (3)

Multiplication and Division•The final answer should have the same number of sig figs as the measurement having the smallest number of sig figs

Ex: 10.305g x 0.00320g=

Ex: 3.64928g/5.2mL=

Addition and Subtraction•Line the numbers up in column

formEx 1: 3.461728 Ex 2: 467.384 14.91 -2.384 0.98001 + 5.2631

Ex 3: 564321 - 264321

Significant Figures SongTo the tune of Three Blind Mice

Verse 1

•Addition and Subtraction line numbers up in columns (Repeat)

•Make sure the decimals are aligned right, Take off the numbers that are on the

right•To get the sig figs (Repeat)

Verse 2

•Multiplication and division count the numbers (Repeat)

•Find the one that is the least That’s the number, the rest will cease•To get the sig figs (Repeat)

Complex Conversions

#1

A heater gives off heat at a rate of 330kJ/min. What is the rate of heat output in kilocalories per hour? (1 cal=4.184J)

#1 Answer

4.7x103 kcal/h

#2

A water tank leaks water at the rate of 3.9mL/h. If the tank is not repaired, what volume of water in liters will it leak in a year?

#2 Answer

34L/yr

#3

At the equator, Earth rotates with a velocity of about 465 m/s. What is the velocity in kilometers per hour? What is the velocity in kilometers per day?

#3 Answer

1670km/hr4.02x104 km/d

Density

Formula

•Density=Mass/Volume•D=m/V•If you know the density triangle, you can

get the formulas for m and V.•The units of density are always going to

have a division sign in them. Ex: g/mL

Question 1

A block has a volume of 25.3cm3. Its mass is 21.7g. Calculate the density of the block.

Answer

0.858g/cm3

Question 2

Isopropyl alcohol has a density of 0.785g/mL. What volume should be measured to obtain 20.0g of the liquid?

Answer

25.5mL

Question 3Ethanol has a density of 0.785g/mL. If you have 105mL, how much mass will it have?

Answer

82.4g