Untitled lesson

Approximate distance of Earth from the Sun:

150,000,000 km

How can we write these

numbers easier?

The solution is

scientific notation.

Approximate mass of a hydrogen atom:

0.00000000000000000000000000167 kilograms.

Learning Outcomes

Explain why scientific
notation is used.

Today, you'll be able to:

Convert scientific notation
to standard form.

Use scientific notation for
real-life figures.

Compare numbers written in
scientific notation.

What is
Scientific
Notation?

Scientific notation is a neat and quick
way of writing

(i) very large or
(ii) very small numbers

a × 10

b
Example: 2.3 × 10

6

Where 1 < α < 10
and b is an integer

Parts of Scientific Notation

coefficient

base

exponent

Exponent ispositive

What do you notice?

Exponent is negative

Scientific Notation to

Standard Form

.

2 3

4

Decimal is moved
6 times to the left

Exponent is positive

. .

1234 5

6

Exponent is negative

1

56

Decimal is moved

6 times to the right

Scientific Notation to

Standard Form

How many times the

human eye blinks

per year?

What is the average

width of a human hair?

How many cell phones

are in use today

in the US?

How wide is a plant

cell in meters?

Can you find out...

The human eye blinks
around 4.2 × 10 times

per year.

The width of a human
hair is approximately

1.17 × 10 cm

Approximately 2.5 × 10
cell phones are in use in

the US.

A plant cell is

approximately 1.276 × 10

meters wide.

= 4,200,0 00

= 250,000,0 00

= 0.0000127 6

= 0.00117

4.2 × 10

2.5 × 10

1.276 × 10
6

6

8

-5
1.17 × 10-3

-3

8

-5

Answer Key

Check the exponent.

1

Based on the exponents, we know

that this is the smallest value.

Ordering Numbers in Scientific Notation

Re-order the numbers.

2

If the exponents are the same,

compare the coefficients.

Since 2 < 3.2, the correct order is:

3

<

<

They both have 4 as their exponent,
so we compare their coefficients.

Ordering Numbers in Scientific Notation

Distance Across

the Universe!

Proxima Centauri, the closest star to our own -
the Sun - is just 40,208,000,000,000 kmaway.

Considering that a light year corresponds to a

distance of 9 × 10 km, which of the two

distances is larger?

12

coefficient

base

exponent

Summary

Scientific Notation

This is a shorter way
of writing large or
small numbers.

Where 1 < α < 10
and b is an integer