Scientific Notation
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www.mathsrevision.com www.mathsrevision.com www.mathsrevision.com Scientific Scientific Notation Notation www.mathsrevision.com Standard form / Scientific Notation Scientific Notation very small numbers Scientific Notation to Number Form
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Scientific Notation. Standard form / Scientific Notation. Scientific Notation to Number Form. www.mathsrevision.com. Scientific Notation very small numbers. Starter Questions. X. www.mathsrevision.com. Scientific Notation. Learning Intention. Success Criteria. - PowerPoint PPT Presentation
Transcript of Scientific Notation
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mScientific Scientific NotationNotation
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m Standard form / Scientific Notation
Scientific Notation very small numbers
Scientific Notation to Number Form
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mStarter QuestionsStarter Questions
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m 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
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com 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 Notation
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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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
10 210
310410
510
110
610
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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
22 10 34 10 47 10 55 10 63 10
This is also known as
Scientific Notation.
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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 25 10
= 8 x 100 000 58 10
= 2 x 10 000 42 10
= 9 x 1 000 000 69 10
= 2 x 1000 32 10
Add the decimal point
A short cut
8 000 000 68 10 ..
Between 1 and 10
The point moved 6 places
Move the point to get a number between 1 and 10
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92 000 000 79.2 10 ..
Add the decimal point
Between 1 and 10
The point moved 7 places
Move the point to get a number between 1 and 10
79.2 10 miles
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mA short cut
2 200 000 000 92.2 10 ..
Add the decimal point Between 1 and
10
The point moved 9 places
Move the point to get a number between 1 and 10
Happy Birthday: Seconds old! 92.2 10
A short cut
228 000 000 82.28 10 ..
Add the decimal point
Between 1 and 10
The point moved 8 places
Move the point to get a number between 1 and 10
82.28 10 years ago!www.
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A short cut
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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
35.3 10 54.7 10
57 10
69.5 10
43 10
71.83 10 53.29 10 62.56 10
101.2 10 69.99 10
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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
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mScientific Scientific NotationNotation
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m Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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.
=86 000 000 78.6 10
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 back
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=346 00053.46 10
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 back
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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
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
1001 10
1 0001 000 0001 000 000 000
31 10 61 10 91 10
one thousand
one million
one billion
one googal !!!
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mStarter QuestionsStarter Questions
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6 9 15 14 5a b a b a
1. Find the highest number that divises into 28 and 14 without leaving a renainder.
2. Simplify
3. Write 55% as a decimal
4. Find the lowest number that both of 5 and 9 divide into without leaving a remainder.
5. 15% of £400
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mScientific Scientific NotationNotation
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m Learning IntentionLearning Intention Success CriteriaSuccess Criteria
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.
Very small numbers!
How wide is an atom?
0.000 000 000 1 metres wide!
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0.000 000 000 1 101 10 .
The point moved 10 places. Negative sign for small numbers.
Move the point to get a number between 1 and 10
-101 10 metres widewww.
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mStandard Form
for small numbers
0.000 000 76 77.6 10 .
The point moved 7 places. Negative sign for small numbers.
Move the point to get a number between 1 and 10
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mStandard Form
for small numbers
Standard Form for small numbers
0.000 001 93 61.93 10 .
The point moved 6 places. Negative sign for small numbers.
Move the point to get a number between 1 and 10
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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
= 0.002
-32 10 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
= 0.000 086
-58.6 10 8.600000.
Hint:Add 5 zeros to the left of
the number.
-5 so remember to move point left for small numbers.
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mChanging back small
numbers
Changing back small numbers
= 0.000 00516
-65.16 10 5.16000000.
Hint:Add 6 zeros to the left of
the number.
-6 so remember to move point left for small numbers.
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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
