Scientific Notation

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Scientific Scientific NotationNotation

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m Standard form / Scientific Notation

Scientific Notation very small numbers

Scientific Notation to Number Form

MTH 4-06b

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Starter QuestionsStarter Questionsww

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com 1. 2.35 + 4 0.25

2. Calculate (- 14)+(- 5)+8

3. What fraction is x:

4. Simplify the fraction

5. Calculate 20% of 210

1680

X

MTH 4-06b

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m Learning IntentionLearning Intention Success CriteriaSuccess Criteria

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

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

Scientific NotationMTH 4-06b

Very large numbers! BOOM!

How far?

92 000 000 miles

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How many seconds in 70 years?

70 years = 2 200 000 000 seconds!

Very large numbers!Happy 70th Birthday!

SPLAT!

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MTH 4-06b

MTH 4-06b

Dinosaurs roamed the earth 228 million years

ago

Very large numbers!

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Short hand !

100 = 10 x 10

1 000 = 10 x 10 x 10

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

10 000 = 10 x 10 x 10 x 10

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

10

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= 10 1

= 10 2

= 10 3

= 10 4

= 10 5

= 10 6

Standard Form200 = 2 x 100

4 000 = 4 x 1000

500 000 = 5 x 100 000

70 000 = 7 x 10 000

3 000 000 = 3 x 1 000 000 This is also known

as Scientific Notation.

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MTH 4-06b

= 2 x 10 2

= 4 x 10 3

= 7 x 10 4

= 5 x 10 5

= 3 x 10 6

Scale of BIG Numbers

http://htwins.net/scale2/

Standard FormExercise 1

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(1)2 000

(2) 20 000

(3) 500

(4) 800 000

(5) 9 000 000

= 5 x 100

= 8 x 100 000

= 2 x 10 000

= 9 x 1 000 000

= 2 x 1000

MTH 4-06b

= 2 x 10 3

= 2 x 10 4

= 5 x 10 2

= 8 x 10 5

= 9 x 10 6

Add the decimal point

A short cut

8 000 000 ..

Between 1 and 10

The point moved 6 places

Move the point to get a number between 1 and 10

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= 8 x 10 6

92 000 000 ..Add the decimal point Between 1 and

10



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= 9.2 x 10 7

9.2 x 10 7 miles

2 200 000 000 ..Add the decimal point Between 1 and

10



Happy Birthday: Seconds old!

A short cutMTH 4-06b

= 2.2 x 10 9

= 2.2 x 10 9

228 000 000 ..Add the decimal point

Between 1 and 10



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A short cutMTH 4-06b

= 2.28 x 10 8

= 2.28 x 10 8 years old

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Standard Form

(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

MTH 4-06b

= 3 x 10 4

= 7 x 10 5

= 5.3 x 10 3

= 4.7 x 10 5

= 9.5 x 10 6

= 18.3 x 10 7

= 3.29 x 10 5

= 2.56 x 10 6

= 1.2 x 10 10

= 9.99 x 10 6

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2 3 5 4 5y x y x xy

1. Find the highest number that divides into 8 and 18 without leaving a remainder.

2. Simplify

3. Write 72% as a decimal

4. Write in scientific notation 230000

5. 30% of £600

MTH 4-06b

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

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

MTH 4-06b

=86 000 000

Zeros after the point aren’t needed.

The point moves 7 places

8.60000000.Hint:

Add 7 zeros, although you probably won’t need

them all.

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Changing backMTH 4-06b

8.6 x 10 7 =

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=346 000

Zeros after the point aren’t needed.

The point moves 5 places

3.4600000.Hint:

Add 5 zeros, although you probably won’t need

them all.

Changing backMTH 4-06b

3.46 x 10 5 =

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Changing back

(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)

56.5 1081.2 10

38 10

63.71 10

56 10

43.3 1067.91 1075.55 1041.05 1093.033 10

= 600 000= 8 000= 650 000= 120 000 000= 3 710 000= 33 000= 7 910 000= 55 500 000= 10 500= 3 033 000 000

MTH 4-06b

Name that number!

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

1 0001 000 0001 000 000 000

one thousand one million one billion one googol !!!

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MTH 4-06b

= 1 x 10 3

= 1 x 10 6

= 1 x 10 9

= 1 x 10 100

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6 9 15 14 5

1. Find the highest number that divides into 28 and 14 without leaving a remainder.

2. Simplify

3. Write 55% as a decimal

4. Find the lowest number that both of 5 and 9

a b a b a

divide into without leaving a remainder.

5. 15% of £400

MTH 4-06b

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

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

MTH 4-06b

Very small numbers!

How wide is an atom?

0.000 000 000 1 metres wide!

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0.000 000 000 1 .The point moved 10 places. Negative sign for small numbers.


-101 10 metres widewww.

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for small numbersMTH 4-06b

= 1 x 10 -10

Scale of SMALL Numbers

http://htwins.net/scale2/

0.000 000 76 .

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


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mStandard Form

for small numbersMTH 4-06b

= 7.6 x 10 -7

Standard Form for small numbers

0.000 001 93 .

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


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= 1.93 x 10 -6

Standard Form for small numbers

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m (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

44.5 10 33.4 10

57 10

47.24 10

43 10

74.94 10 59.5 10 89.8 10 41.03 10 106.6 10

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= 0.002

2000.

Hint:Add 3 zeros to the left of

the number.

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

.

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mChanging back small

numbers MTH 4-06b

2 x 10 -3 =

= 0.000086

8 600000.


the number.


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mChanging back small

numbers MTH 4-06b

8.6 x 10 -5 = .

Changing back small numbers

= 0.000 00516

5 16000000.


the number.


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MTH 4-06b

5.16 x 10 -6 = .

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m (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)

35.8 1076.2 10

59 10

66.45 10

45 10

75.3 1069.17 1032.12 1052.03 1096.032 10

= 0.000 5= 0.000 09= 0.005 8= 0.000 000 62= 0.000 006 45= 0.000 000 53= 0.000 009 17= 0.002 12= 0.000 020 3= 0.000 000 006 032

Changing back small numbers MTH 4-06b

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Scientific Notation