Section 5.1 Scientific Notation and Units 1.To show how very large or very small numbers can be expressed in scientific notation 2.To learn the English,

Section 5.1

Scientific Notation and Units

1. To show how very large or very small numbers can be expressed in scientific notation

2. To learn the English, metric, and SI systems of measurement

3. To use the metric system to measure length, volume and mass

Objectives

Section 5.1


A. Scientific Notation

• Very large or very small numbers can be expressed using scientific notation – The number is written as a number between 1 and 10

multiplied by 10 raised to a power.

e.g. 7200 is 7.2 x 103

– The power of 10 depends on:• The number of places the decimal point is moved.

• The direction the decimal point is moved.

Left Positive exponentRight Negative exponent

size slider smallsize large size

Section 5.1



• Representing Large Numbers

93,000,000 miles from the Earth to the Sun (sunlight takes 8 minutes to reach us)

93,000,000 = 9.3 x 10,000,000= 9.3 x 10 x 10 x 10 x 10 x 10 x 10 x 10= 9.3 x 107 (Decimal point moved 7 digits to the left)

Number between 1 and 10

Appropriate power of ten

Section 5.1



• Representing Small Numbers

0.000167

To obtain a number between 1 and 10 we must move the decimal point to the right.

0.000167 = 1.67 10-4

10-4 = 1/10000 (one ten-thousandth)

Section 5.1


Convert the following numbers between normal and scientific notation:

329

700,000

20090

0.000034

0.01023

123.4

45.607

1.7 x 103

2.4503 x 105

7.9 x 1011

2.8 x 10-3

7.45 x 10-1

2.3 x 10-7

Section 5.1


Convert the following numbers/sums into correct scientific notation:

35.9 x 103

556.67 x 104

22.7 x 10-3

0.0348 x 10-1

1845 x 105

123.4 x 1023

0.00345 x 107

Section 5.1


Scientific Notation Math - Exponents

103

10-5

100

1/103

1/105

1/10-2

1/10-7

103 x 108

10-3 x 107

10-5 x 10-3

105 / 102

10-7 / 105

10-2 / 10-4

Section 5.1


Scientific Notation Math

Multiplication

- multiply the numbers, add the indices

1.2 x 104 multiplied by 5 x 106 =

Division

- divide the numbers, subtract the indices

5.5 x 108 divided by 1.1 x 102 =

(For all operations reconvert answers to full scientific notation)

Section 5.1


Scientific Notation Math

• Addition or subtraction:

Convert to the same base and perform the operation

Then reconvert to scientific notation

1.04 x 103 plus 6.8 x 102 =

Section 5.1


Combined Operations – Give the answer in scientific notation

7.5 x 105

__________

3 x 103

2 x 106 x 1.5 x 102

________________________

5 x 103

6.5 x 105 x 4 x 104

________________________

2 x 10-3

7.5 x 10-5

______________________

3 x 103 x 5 x 10-6

Section 5.1


B. Units

• Units provide a scale on which to represent the results of a measurement. What units can you think of?

“Time is God’s way of making sure everything doesn’t happen at once” (Unknown)

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B. Units • There are 3 commonly used unit systems.

– English (used in the United States)– Metric (broadly used across the World) – SI (most formal version of Metric used in science)

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Countries not yet officially metric: USA, Liberia, Myanmar

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Metric/SI Prefixes

Prefixes are used to denote different sizes of each unit:

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Full List of Metric Prefixes

Multiplication factor (scientific notation)

Prefix Symbol

(1024) yotta Y

(1021) zetta Z

(1018) exa E

(1015) peta P

(1012) tera T

1 000 000 000 (109) giga G

1 000 000 (106) mega M

1000 (103) kilo k

100 (102) hecto h

10 (101) deka da

0.1 (10-1) deci d

0.01 (10-2) centi c

0.001 (10-3) milli m

0.000 001 (10-6) micro µ

0.000 000 001 (10-9) nano n

(10-12) pico p

(10-15) femto f

(10-18) atto a

(10-21) zepto z

(10-24) yocto y

Section 5.1


Metric Dollars

100 dollars1 hectodollar

1x102

1 dime1 decidollar

1X10-1

1 cent1 centidollar

1X10-2

10 dollars1 dekadollar

1x101

1 dollar1 dollar1x100

Section 5.1


C. Measurements of Length, Volume and Mass

• Length– Fundamental unit is the meter – 1 meter = 39.37 inches

Who is taller – a woman 5 ft 6 inches or a man 1.62 meters tall?

Comparing English and metric systems

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**

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• Volume – Amount of 3-D space occupied by a

substance – Fundamental unit is meter3 (m3)

1 liter = 2.11 Pints

250mL of milk is close to ½ Pint, 1 Pint, 1 Quart, 1 Gallon?

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• Mass – Quantity of matter in an object – Fundamental unit is kilogram = 2.2 lbs

Section 5.1



How many quarters in a row to make a meter?

What is the weight in kg of a man who weighs 180 lbs?

How many liters in a six-pack of soda cans?

Documents

Section 5.1 Scientific Notation and Units 1.To show how very large or very small numbers can be expressed in scientific notation 2.To learn the English,