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Standard Form What is Standard Form 43620 Interactive 12.7 Million to Standard Form 4.362 x 10 7 5.084 x 10 2 Interactive 0.0005362 0.781 Light Year Intro.

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Presentation on theme: "Standard Form What is Standard Form 43620 Interactive 12.7 Million to Standard Form 4.362 x 10 7 5.084 x 10 2 Interactive 0.0005362 0.781 Light Year Intro."— Presentation transcript:

1 Standard Form What is Standard Form Interactive 12.7 Million to Standard Form x x 10 2 Interactive Light Year Intro Light Year Calculation Six Questions Standard Form to Large Six Questions Expressing Small Numbers in Standard Form Small SF to normal

2 How far is it from the Earth to the Sun BOOM! How far? miles

3 Some calculations result in very Large answers How many seconds in 70 years? 70 years = seconds! Happy 70 th Birthday! SPLAT!

4 Using millions to understand the size Dinosaurs roamed the earth 228 million years ago Dinosaurs roamed the earth years ago

5 Number is different formats CostSavers made a profit of £ MegaSales made a profit of £ CostSavers made a profit of £7.5 Million MegaSales made a profit of £ 1.23 Million or Do you need to write all the ZEROS to make sense of the number

6 Standard Form A number in STANDARD FORM has two parts x x x x 18 Number between 1 and …. xPower of 10

7 Making sense of the code 100 = 10 x = 10 x 10 x = 10 x 10 x 10 x 10 x = 10 x 10 x 10 x = 10 x 10 x 10 x 10 x 10 x 10 10

8 Not beginning with = 2 x 10 x = 4 x 10 x 10 x = 7 x 10 x 10 x 10 x = 3 x 10 x 10 x 10 x 10 x 10 x 10 This is also known as Scientific Notation. 2x 10 2 = 4 x 3 4 x 7 = = 3 x = 6

9 Whole No to SF (1)2 000 (2) (3) 500 (4) (5) = 5 x 10 x 10 = 8x10x10x10x10x10 = 2 x 10x10x10x10 = 9x10x10x10x10x10x10 = 2 x 10 x 10 x 10

10 43620 to STANDARD FORM x Move your finger, from point, until you get a whole number less than 10 Copy figure then add a point Copy other figure until all that is to be copied is zeros Add x 10

11 To change to STANDARD FORM x Count number of places from new position to old position This number goes above the 10 to indicate how often you multiply by 10

12 to STANDARD FORM 2 x Move your finger, from point, until you get a whole number less than 10 Copy figure then add a point Copy other figure until all that is to be copied is zeros Add x 10

13 To change to STANDARD FORM 2 x Count number of places from new position to old position This number goes above the 10 to indicate how often you multiply by

14 907.5 to STANDARD FORM 3 x Move your finger, from point, until you get a whole number less than 10 Copy figure then add a point Copy other figure until all that is to be copied is zeros Add x 10 5

15 To change to STANDARD FORM 3 x Count number of places from new position to old position 2 This number goes above the 10 to indicate how often you multiply by = x 10 2

16 Large To SF Interactive x10^5 C. ÷x On ² - Ans = √ (-) ^Exp x New Example 0 Test

17 Large to SF Examples x10^6 C. ÷x On ² - Ans = √ (-) ^Exp 5.27 x10 4 (a) x10 6 (b) x10 8 (c) x10 6 (d) x10 3 (e) x10 5 (f) New

18 12.7 Millions to SF Change 12.7 million to Standard Form x million would have 6 zeros. Write down 12 then an underline where the zeros would have been Add any figures after the point above the underline then fill remainder with zeros NOW CHANGE TO STANDARD FORM 12.7 million = = 1.27 x

19 Millions to SF Change 7¾ million to Standard Form x million would have 6 zeros. Write down 7 then an underline where the zeros would have been Add any figures after the point above the underline then fill remainder with zeros NOW CHANGE TO STANDARD FORM 7¾ million = 7.75 x ¾ million = 7.75 million

20 Millions to SF : Examples C. ÷x 0 + On ² - Ans = √ (-) ^Exp 5.3 x10 6 (a) 5.3 million 1.3 x10 6 (b) 1.3 million 4.9 x10 7 (c) 49 million 7.8 x10 7 (d) 78 million 7 x10 6 (e) 7 million 1.6 x10 7 (f) 16 million New

21 Standard Form to Normal x = To multiply a whole number by 10 just add a zero In Standard form the power of 10 ( small number above the 10 ) tells you how often to multiply by 10. Click the arrow to see some simple examples Normally the 1 st number includes a point.

22 What is …… ? = x 10 3 (1) = x 10 3 (2) = x 10 5 (3) = x 10 2 (4) = x 10 8 (5) = x 10 6 (6)

23 SF to Normal x = = = = 750 = = = = x 10 4 T Next Finish Multiplying by a +ve power of 10 moves the point to the right

24 Back to Normal x Start as if there were no figures after point You have to multiply by 10 seven times. Instead of adding 7 zeros put 7 underlines Copy other figure until all that is to be copied is zeros 7 4 Fill remaining places with zeros = The “lines” show where the point should go

25 Back to Normal x Start as if there were no figures after point You have to multiply by 10 twice Instead of adding 2 zeros put 2 underlines Copy other figure until all that is to be copied is zeros x = The “lines” show where the point should go 2 = 502.4

26 Large SF to normal C. ÷x 0 + On ² - Ans = √ (-) ^Exp x New Example 0 Test Place Point

27 SF to Normal Examples x10^6 C. ÷x On ² - Ans = √ (-) ^Exp 4.73 x10 3 (a) x10 3 (b) x10 5 (c) x10 5 (d) x10 3 (e) x10 5 (f) New

28 Small Numbers How wide is an atom? metres wide! Small numbers like this will have negative powers of 10

29 Introducing Small 3.9 x = = = 39 0 = 39. = x10 -2 = x10 -3 = x10 -4 = x T Next Number >=1 …….. Power of 10 will be positive Number between 0 and 1 …….. Power of 10 will be negative

30 Small to SF x = Next Examples Click number to convert. Numbers from 0 to 1 have negative powers. Compare number of zeros at front to the power.

31 6 2 Small Numbers x Ignore the zeros at the front then cover until you get a number less than 10 Copy figure, add a point then other figure until all that is left are zeros Add x 10 0 The original position of the point is to THE LEFT Count …. 1 to left …. -1 …. 2 to left ….. -2 and so on = x 10 -4

32 1 Small Numbers x Ignore the zeros at the front then cover until you get a number less than 10 Copy figure, add a point then other figure until all that is left are zeros Add x 10 The original position of the point is to THE LEFT Count …. 1 to left …. -1 …. 2 to left ….. -2 and so on = 7.81 x 10

33 Small To SF Interactive C. ÷x 0 + On ² - Ans = √ (-) ^Exp x New Example 0 Test Click top no then click destination. Use arrows to set power

34 Small to SF Examples C. ÷x 0 + On ² - Ans = √ (-) ^Exp 1.42 x10 -6 (a) x10 -3 (b) x10 -4 (c) x10 -3 (d) x10 -3 (e) x10 -8 (f) New

35 8.437 x = = = = = x10 -2 = x10 -3 = x10 -4 = x T Next When the power is negative the point moves to left There will be the same no of zeros at front as power Small SF to Normal

36 x Start as if there were no figures after point Positive means GO RIGHT ….. Negative means GO LEFT Need 8 underline going left starting under the 7 …. -8 …. 8 to LEFT Copy other figure after the = The “lines” show where the point should go

37 Small SF to normal C. ÷x 0 + On ² - Ans = √ (-) ^Exp x New Example 0 Test Place Point

38 Small SF to Normal Examples C. ÷x 0 + On ² - Ans = √ (-) ^Exp 7.42 x10 -5 (a) x10 -5 (b) x10 -8 (c) x10 -6 (d) x10 -4 (e) x10 -4 (f) New

39 Positive Powers x10^6 C. ÷x On ² - Ans = √ (-) ^Exp 1.2 x10 6 (a) x10 5 (b) x10 6 (c) x10 5 (d) x10 5 (e) x10 3 (f) 3420 New

40 Negative Powers x10^6 C. ÷x On ² - Ans = √ (-) ^Exp 7.82 x10 -5 (a) x10 -5 (b) x10 -4 (c) x10 -8 (d) x10 -3 (e) x10 -6 (f) New

41 Mixed Powers x10^6 C. ÷x On ² - Ans = √ (-) ^Exp 7.36 x10 4 (a) x10 -3 (b) x10 8 (c) x10 3 (d) x10 6 (e) x10 -4 (f) New

42 Light Year How far is it to the Town Centre? 5 minutes by car or about 20 minutes walk. How far is it to Glasgow? About 20 minutes by car? How far is it to London ? About 400 miles by road taking about 7 hours or about 5 hours by train Sometimes the time a journey takes is a better indication of the distance.

43 Light Years Distances in the solar system are vast. Distance from the Sun to Pluto is km or 5.95 x km To make sense of distance people often use time. For these extremely large distances scientists use the time that Light takes to go from one point to another As a comparison light takes about 1.27 seconds to go from the Moon to Earth. Light takes 4 Hours and 2 minutes to go from Pluto to the Earth About times the time so about the distance

44 Distances around the Universe The distance from the Sun to the Earth is km or 1.5 x 10 8 km It is hard to make sense of this distance The distance round the equator is about km or 380 hours (nearly 16 days ) by car. The distance from Sun to Earth is about times a journey round the equator or 174 year by car Scientist need to compare these distances and as there are no roads in space they use one quantity that can move there LIGHT

45 Time for light to travel from Earth to the moon sec Earth to Mars 4 min 10 sec Earth to Venus 5 min 10 sec Earth to Mercury 2 min 20 sec 8 min 20 sec Earth to the Sun Earth to Jupiter 35 min Earth to Saturn 71 min Earth to Uranus 2 hr 31 min Earth to Pluto 4 hrs 2 min If a spacecraft could travel at the speed of light it would take about 1.3 seconds to get to the moon The distance from Earth to Pluto is like RETURN journeys to the moon

46 4.22 Light Years x km Proxima Centauri is the closest star to the Solar System. It is 4.22 Light years away If it was possible to build a craft which could travel at the speed of light it would take over 4 years to get to this star. 4 hours into the journey it would pass Pluto having completed about 1 / 365 part of the journey 1 Light Year is x km Distance to Proxima Centauri is 4.22 Light Year 4.22 Light Year 4.22 x 4.22 x =3.995 x km x 10 x x 9.47 E x9.47 x =

47 7 Light Years x km 7 Light Year 7 Light Year 7 x 7 x =6.629 x km x 10 x 12 7 x 9.47 E 12 7x9.47 x = x km 32 Light Year 32 Light Year 32 x 32 x = x km x 10 x x 9.47 E 12 32x9.47 x =

48 Light Year Calculations C. ÷x 0 + On ² - Ans = √ (-) ^Exp 1 Light Year is x km Light Year = 6.1 x9.467 Exp 12 = On Next 6.1 x ( x ) km 6.1 = x 10 = Click after using calculator

49 Light Year Speed of Light is m/s In 1 second Light travels a distance of 300 million metres or km In 1 hour Light travels a distance of km or Million Km or 1.08 x 10 9 km In 1 year Light travels a distance of km or Million Km or 9.47 x km To make sense it may be better to relate this to distances in the Universe

50 One Light Year


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