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### Scientific Notation

### Scientific Notation

### Scientific Notation

Standard form / Scientific Notation

Scientific Notation to Number Form

www.mathsrevision.com

Scientific Notation very small numbers

www.mathsrevision.com

MTH 4-06b

Learning Intention

Success Criteria

- To understand and use the quick method to put large numbers into scientific notation.

- To show a very quick way of putting a large number in scientific notation very quickly.

www.mathsrevision.com

www.mathsrevision.com

Happy 70th Birthday!

How many seconds in 70 years?

Very large numbers!

MTH 4-06b

SPLAT!

www.mathsrevision.com

70 years = 2 200 000 000 seconds!

MTH 4-06b

Dinosaurs roamed the earth 228 million years ago

www.mathsrevision.com

MTH 4-06b

= 10 1

10

= 10 2

100 = 10 x 10

= 10 3

1 000 = 10 x 10 x 10

= 10 4

10 000 = 10 x 10 x 10 x 10

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= 10 5

100 000 = 10 x 10 x 10 x 10 x 10

= 10 6

1 000 000 = 10 x 10 x 10 x 10 x 10 x 10

MTH 4-06b

= 2 x 10 2

200 = 2 x 100

= 4 x 10 3

4 000 = 4 x 1000

= 7 x 10 4

70 000 = 7 x 10 000

= 5 x 10 5

500 000 = 5 x 100 000

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= 3 x 10 6

3 000 000 = 3 x 1 000 000

This is also known as

Scientific Notation.

Scale of

BIG Numbers

Exercise 1

MTH 4-06b

- 2 000
- (2) 20 000
- (3) 500
- (4) 800 000
- (5) 9 000 000

= 2 x 10 3

= 2 x 1000

= 2 x 10 4

= 2 x 10 000

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= 5 x 10 2

= 5 x 100

= 8 x 10 5

= 8 x 100 000

= 9 x 10 6

= 9 x 1 000 000

Add the

decimal point

Between 1 and 10

A short cut

MTH 4-06b

Move the point to get a

number between 1 and 10

= 8 x 10 6

.

8 000 000

.

www.mathsrevision.com

Add the

decimal point

Between 1 and 10

A short cut

MTH 4-06b

Move the point to get a

number between 1 and 10

= 9.2 x 10 7

.

92 000 000

.

www.mathsrevision.com

9.2 x 10 7 miles

Add the

decimal point

Between 1 and 10

A short cut

MTH 4-06b

Move the point to get a

number between 1 and 10

= 2.2 x 10 9

.

2 200 000 000

.

Happy Birthday: Seconds old!

= 2.2 x 10 9

Add the

decimal point

Between 1 and 10

A short cut

MTH 4-06b

Move the point to get a

number between 1 and 10

= 2.28 x 10 8

228 000 000

.

.

www.mathsrevision.com

= 2.28 x 10 8 years old

MTH 4-06b

= 3 x 10 4

(1) 30 000

(2) 700 000

(3) 5 300

(4) 470 000

(5) 9 500 000

(6) 18 300 000

(7) 329 000

(8) 2 560 000

(9) 12 000 000 000

(10) 9 990 000

= 7 x 10 5

= 5.3 x 10 3

= 4.7 x 10 5

= 9.5 x 10 6

= 18.3 x 10 7

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= 3.29 x 10 5

= 2.56 x 10 6

= 1.2 x 10 10

= 9.99 x 10 6

Learning Intention

Success Criteria

- Know how to expand large numbers in scientific notation to number format.

- To understand how to change large numbers from Scientific Notation to number form.

www.mathsrevision.com

www.mathsrevision.com

Zeros after the point aren’t needed.

Changing back

MTH 4-06b

8.6

0000000

.

=86 000 000

8.6 x 10 7 =

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Hint:

Add 7 zeros, although you probably won’t need them all.

Zeros after the point aren’t needed.

Changing back

MTH 4-06b

3.46 x 10 5 =

3.46

00000

.

=346 000

www.mathsrevision.com

Hint:

Add 5 zeros, although you probably won’t need them all.

MTH 4-06b

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

= 600 000

= 8 000

= 650 000

= 120 000 000

= 3 710 000

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= 33 000

= 7 910 000

= 55 500 000

= 10 500

= 3 033 000 000

MTH 4-06b

= 1 x 10 3

1 000

one thousand

= 1 x 10 6

1 000 000

one million

= 1 x 10 9

1 000 000 000

one billion

10 000 000 000 000 000 000

000 000 000 000 000 000 000

000 000 000 000 000 000 000

000 000 000 000 000 000 000

000 000 000 000 000 000

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one googol !!!

= 1 x 10 100

Learning Intention

Success Criteria

- Know how to change very small numbers into scientific notation and how to do the reverse process.

- To understand how to change very small numbers into Scientific Notation and vice versa.

www.mathsrevision.com

www.mathsrevision.com

MTH 4-06b

www.mathsrevision.com

How wide is an atom?

0.000 000 000 1 metres wide!

The point moved 10 places. Negative sign for small numbers.

Standard Form

for small numbers

MTH 4-06b

Move the point to get a

number between 1 and 10

= 1 x 10 -10

.

0.000 000 000 1

www.mathsrevision.com

Scale of

SMALL Numbers

The point moved 7 places. Negative sign for small numbers.

Standard Form

for small numbers

MTH 4-06b

Move the point to get a

number between 1 and 10

= 7.6 x 10 -7

.

0.000 000 76

www.mathsrevision.com

The point moved 6 places. Negative sign for small numbers.

Standard Form

for small numbers

MTH 4-06b

Move the point to get a

number between 1 and 10

= 1.93 x 10 -6

0.000 001 93

.

www.mathsrevision.com

for small numbers

MTH 4-06b

(1) 0. 000 3

(2) 0.000 07

(3) 0.000 45

(4) 0.003 4

(5) 0. 000 724

(6) 0.000 000 494

(7) 0.000 095

(8) 0.000 000 098

(9) 0.000 1 03

(10) 0.000 000 000 66

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-3 so remember to move point left for small numbers.

Changing back small numbers

MTH 4-06b

Hint:

Add 3 zeros to the left of the number.

2 x 10 -3 =

2

000

.

.

www.mathsrevision.com

= 0.002

-5 so remember to move point left for small numbers.

Changing back small numbers

MTH 4-06b

Hint:

Add 5 zeros to the left of the number.

.

8.6 x 10 -5 =

8 6

00000

.

www.mathsrevision.com

= 0.000086

-6 so remember to move point left for small numbers.

Changing back small numbers

MTH 4-06b

Hint:

Add 6 zeros to the left of the number.

5.16 x 10 -6 =

.

5 16

000000

.

www.mathsrevision.com

= 0.000 00516

MTH 4-06b

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

= 0.000 5

= 0.000 09

= 0.005 8

= 0.000 000 62

= 0.000 006 45

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= 0.000 000 53

= 0.000 009 17

= 0.002 12

= 0.000 020 3

= 0.000 000 006 032

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