Scientific Notation

Scientific Notation

Scientific Notation was developed so that scientists in particular, could easily work with very large and very small numbers.

Large Numbers

Understand: when a number does not show the decimal point, it is understood to be located after the last digit on the right.

Our Milky Way galaxy has about 120 000 000 000 stars. Where is the decimal point?

The estimated age of the earth ~ 4 500 000 000 years

Where is the decimal point?

The temperature of the sun’s interior is 1 300 000 C

Where is the decimal point?

Now, let’s start the first handout together and complete for homework.

Next day: Let’s correct the homework and then read page two together. Complete the exercises as seatwork.

Page three has Large Numbers written in both Scientific Notation and Standard Notation. Follow the models below before completing the Large Numbers portion of page three.

7.4 x 103 = 7400. 1400 = 1.4 x 103

Small Numbers

The diameter of a virus is about 0.000 000 1 metres

We convert to scientific notation in the following manner:

0.  000 000 1 = 1.0 x 10-?

-  we move the decimal point to the right of the first whole number.

-  next, we count how many places to the left we would have to move the decimal point to return the point to its original place: 7 places to the left.

-  moving to the left means we will have a negative exponent.

0.000 000 1 = 1.0 x 10-7

The mass (amount of matter) of a hydrogen atom is about

0.000 000 000 000 000 000 000 00167 grams

Scientific Notation: 1.67 x 10-24

Understand: all whole numbers must be included when converting to scientific notation.

We must also convert from Scientific Notation to Standard Notation. Do so in the following manner:

8.67 x 10-5 = .0000867

Practice:

1) 0.0043 =

2) 0.0375 =

3) 4.21 x 10-3 =

4) 611 x 10-5 =

Now, complete the Small Numbers portion of page three.

Next, from the Textbook:

Page 39 - do 2

Page 40 - 1 2 3 4 9

Challenge

Understand:

1 km = 1000 m. It is 10³ more than metres

So

1.383 x 106 km is also 1.383 x 109m

(10³ more)

1m = 100cm. It is 10² more than centimetres

So

4.35 x 10-13 m is also 4.35 x 10-11 cm

IMP - we move the exponent closer to zero to increase the value. So, 10-2 is more, not 10².

Textbook: Page 40 - do 5 7

Word problems:

1) Compare: 4.2 x 10-3

42.3 x 10-4

0.421 x 10-2

To compare, convert to standard notation and arrange from least to greatest.

2) An article stated that Mercury is 5.8 x 10-7

km from the sun. Is this reasonable or not? Explain

Interesting facts:

-  The TEM microscope provides a view of less than 1 micrometer or 1.0 x 10-6 in thickness, which is

0.000 001of a metre

-  1 nanometer(nm)= 1.0 x 10-9 which is

0.000 000 001 of a metre

-  1 picometer = 1.0 x 10-12 which is

0.000 000 000 001 of a metre

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