1. Standard Form What is Standard Form Six Questions Interactive 43620
12.7 Million to Standard Form
Standard Form to Large
Interactive 7 2
4.362 x 10
5.084 x 10
Six Questions
Expressing Small Numbers in Standard Form
0.781
Small SF to normal
Light Year Intro
Light Year Calculation

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

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

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

5. Number is different formats
CostSavers made a profit of £
MegaSales made a profit of £ or
CostSavers made a profit of £7 .5 Million
MegaSales made a profit of £ 1.23 Million
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 7 1.01 1.01 x 1012
1.01
5.038 x 10 -8
1.01
2.79 x 10 18
1.01
9.999 x 10
Number between 1 and …. x
Power of 10

7. Making sense of the code10
100 = 10 x 10
1 000 = 10 x 10 x 10
= 10 x 10 x 10 x 10
= 10 x 10 x 10 x 10 x 10
= 10 x 10 x 10 x 10 x 10 x 10

8. Not beginning with 1 10 2 x = 10 4 x = 10 x = 7 10 3 x = 2 3 4 6
= 3 x 10 x 10 x 10 x 10 x 10 x 10 =
This is also known as
Scientific Notation.

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

10. 43620 to STANDARD FORM 4 3 6 2 4 3 6 2 x 10
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 FORM4 3 6 2 4 2 1 3 4 3 6 2 x 10
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 3 8 2 3 8 2 x 10
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 23 8 2 5 6 4 2 1 3 3 8 2 x 10
Count number of places from new position to old position
This number goes above the 10 to indicate how often you multiply by 10

14. 907.5 to STANDARD FORM 3 9 7 5 9 7 5 x 10
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

15. To change to STANDARD FORM 39 7 5 2 1 9 7 5 x 10
Count number of places from new position to old position
This number goes above the 10 to indicate how often you multiply by 10 2
907.5 = x 10

16. Large To SF Interactive5 8 9 1 5 x 10 4 6 x 6
New Example
Test
(-) √ C x ÷ ^
Exp
7.53x10^5 5 6 7 8 9 + - On
753000 1 2 3 4 . =
Ans

17. Large to SF Examples 5 5 4 6 6 x 7.84x10^6 7840000 (a) 52700 5.27 x 10
(b) 5
6.65 x 10 5 8
(c)
2.4 x 10 4 6 6 6 x
6.89 x 10
(d) 3
4510
(e)
4.51 x 10 5
805000
8.05 x 10
(f)
(-) √ C x ÷ ^
Exp
New
7.84x10^6 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

18. 12.7 Millions to SF
Change 12.7 million to Standard Form 1 2 7 6 5 7 1 2 3 4 1 2 7 x 10
12 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 7
12.7 million = = 1.27 x 10

19. Millions to SF 7 7 5 7 7 5 x 10 7¾ million = 7.75 million
Change 7¾ million to Standard Form
7¾ million = 7.75 million 7 7 5 6 3 4 5 1 2 7 7 5 x 10
7 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 6
7¾ million = 7.75 x 10

20. Millions to SF : Examples6
(a)
5.3 x 10
5.3 million 6 5
(b)
1.3 x 10 5
1.3 million 7
(c)
49 million
4.9 x 10 4 6 x 6 7
78 million
(d)
7.8 x 10 6
7 million
(e) 7 x 10 7
16 million
1.6
(f) x 10
(-) √ C x ÷ ^
Exp
New 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

21. Standard Form to Normal
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 9 1 x 10 = 1
Normally the 1st number includes a point.

22. What is …… ?
6 x 10 3
= 600
(1)
8 x 10 3
= 8 000
(2)
4 x 10 5 =
(3)
7 x 10 2
= 700
(4)
3 x 10 8 =
(5)
9 x 10 6 =
(6)

23. 4
SF to Normal T . 5
x 10 3 7 1 1
3.715x10 3 7 . 1 5 3 3 3 3 3 = 2
3.715x10 = 3 7 1 . 5 9 9 9 9 9 3
3.715x10 = 3 7 1 5 . 6 4
3.715x10 3 7 1 5 . = 5
7.218x10 = 7 2 1 8 . 6 6 6
7.218x10 7 2 1 8 . 6 6 = 7
7.218x10 7 2 1 8 . 6 = 8
7.218x10 7 2 1 8 . = 4 3 7 1 5
3.715 x 10
Multiplying by a +ve power of 10 moves the point to the right
Finish
Next

24. Back to Normal 7 4 3 6 2 x 10 = 4 3 6 2
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
The “lines” show where the point should go
Copy other figure until all that is to be copied is zeros
Fill remaining places with zeros

25. Back to Normal 2 5 8 4 x 10 4 = 5 8
Start as if there were no figures after point
You have to multiply by 10 twice Instead of adding 2 zeros put 2 underlines
The “lines” show where the point should go
Copy other figure until all that is to be copied is zeros 2
5.084 x 10
= 502.4

26. Large SF to normal 6 3 8 6 4 x 10 5 3 6 5 4 6 x 6 6 . New Example Test3 6 5 4 6 x 6
New Example
Test
Place Point
(-) √ C x ÷ ^
Exp 6 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

27. SF to Normal Examples 5 5 4 6 x 6 7.84x10^6 7840000 (a) 4.73 x 10 4730
(b) 5
9.62 x 10
9620 5 5
(c)
6.47 x 10
647000 4 6 5 x 6
873000
(d)
8.73 x 10 3
3160
(e)
3.16 x 10 5
277000
2.77 x 10
(f)
(-) √ C x ÷ ^
Exp
New
7.84x10^6 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

28. Small Numbers How wide is an atom? 0.000 000 000 1 metres wide!
Small numbers like this will have negative powers of 10

29. Introducing Small T . x 10 3 9 3.9x10 7 6 3 9 . _ _ = 3.9x10 = 6 3 9 .8
Introducing Small T .
x 10 3 9 3
3.9x10 7 6 3 9 . _ _ = 2
3.9x10 = 6 3 9 . 7 _ _ 1 .
3.9x10 = 3 9 5 7 _ _
3.9x10 3 . 9 5 7 _ _ = -1
3.9x10 = . 3 9 5 7 _ _ -2
3.9x10 . 3 9 5 7 _ _ = -3
3.9x10 . 3 9 5 7 _ _ = -4 .
3.9x10 3 9 5 7 _ = 8
Number >=1 …….. Power of 10 will be positive 3 1
3.9 x 10
Number between 0 and 1 …….. Power of 10 will be negative
Next

30. Small to SF
0.15
0.39 = -6
4.42 x 10
0.97
0.1
0.0596
0.012
Click number to convert. Numbers from 0 to 1 have negative powers. Compare number of zeros at front to the power.
Next Examples

31. Small Numbers 5 3 6 2 -1 -2 -3 -4 5 3 6 2 x 10
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 -4
= x 10

32. Small Numbers 7 8 1 -1 7 8 1 x 10
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 -1
0.781 = 7.81 x 10

33. Small To SF Interactive5 8 7 9 5 5 x 10 4 6 x 6
Click top no then click destination.
Use arrows to set power
New Example
Test
(-) √ C x ÷ ^
Exp 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

34. Small to SF Examples -6
(a)
1.42 x 10 -3 5
(b)
6.27 x 10 5 -4
(c)
7.5 x 10 4 6 x 6 -3
0.0012
(d)
1.2 x 10 -3
(e)
9.33 x 10 -8
3.88
(f) x 10
(-) √ C x ÷ ^
Exp
New 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

35. Small SF to Normal T . 4 3 7 x 10 8 8.437x10 7 6 8 4 3 7 . _ _ =7 6 8 4 3 7 . _ _ = 2
8.437x10 = 6 8 4 3 . 7 _ _ 1
8.437x10 = 8 4 . 3 7 _ _
8.437x10 8 . 4 3 7 _ _ = -1
8.437x10 = . 8 4 3 7 _ _ -2
8.437x10 . 8 4 3 7 _ _ = -3
8.437x10 . 8 4 3 7 _ _ = -4
8.437x10 . 8 4 3 7 _ = 4
When the power is negative the point moves to left 8 1
8.437 x 10
There will be the same no of zeros at front as power
Next

36. Small SF to Normal -8 7 8 3 x 10 7 8 3 =
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
The “lines” show where the point should go
Copy other figure after the 7

37. Small SF to normal -6 2 8 5 1 x 10 5 7 5 1 5 4 6 x 6 6 . New Example7 5 1 5 4 6 x 6
New Example
Test
Place Point
(-) √ C x ÷ ^
Exp 6 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

38. Small SF to Normal Examples-5
(a)
7.42 x 10 -5 5
(b)
7.01 x 10 5 -8
(c)
1.03 x 10 4 6 -6 x 6
(d)
3.21 x 10 -4
(e)
8.91 x 10 -4
2.38
(f) x 10
(-) √ C x ÷ ^
Exp
New 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

39. Positive Powers 5 5 4 6 x 6 7.84x10^6 7840000 (a) 1.2 x 10 1200000 (b)
9.24 x 10
924000 5 6
(c)
7.1 x 10 4 6 x 6 5
(d)
562000
5.62 x 10 5
(e)
418000
4.18 x 10 3
(f)
3420
3.42 x 10
(-) √ C x ÷ ^
Exp
New
7.84x10^6 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

40. Negative Powers 5 5 4 6 x 6 7.84x10^6 7840000 (a) 7.82 x 10 0.0000782-5
(a)
7.82 x 10 -5 5
(b)
6.58 x 10 5 -4
(c)
5.43 x 10 4 6 x 6 -8
(d)
9.13 x 10 -3
(e)
2.06 x 10 -6
(f)
2.39 x 10
(-) √ C x ÷ ^
Exp
New
7.84x10^6 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

41. Mixed Powers 4
(a)
7.36 x 10
73600 -3 5
(b)
8.84 x 10 5 8
(c)
6.49 x 10 4 6 x 6 3
(d)
5280
5.28 x 10 6
(e) 8 x 10 -4
3.11
(f) x 10
(-) √ C x ÷ ^
Exp
New
7.84x10^6 5 6 7 8 9 + - On 1 2 3 4 . =
Ans

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 1010 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 108 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
8 min 20 sec
Earth to the Sun
Earth to Mercury
5 min 10 sec
Earth to Venus
2 min 20 sec
Earth to the moon
1.268 sec
Earth to Mars
4 min 10 sec
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
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 1012 km
Distance to Proxima Centauri is 4.22 Light Year
4.22
Light Year
9.467 x 1012 km
4.22x9.47 x 1012 =
4.22 x 9.47 E 12
4.22 x
x 10x 12
4.22 x 9.467
=3.995 x 1013 km

47. 7 Light Years 7 Light Year 7 Light Year 9.467 x 1012 km
7x9.47 x 1012 =
7 x 9.47 E 12
7 x
x 10x 12
7 x 9.467
=6.629 x 1013 km
32 Light Year 32
Light Year
9.467 x 1012 km
32x9.47 x 1012 =
32 x 9.47 E 12
32 x
x 10x 12
32 x 9.467
= x 1014 km

48. Light Year Calculations
1 Light Year is x 1012 km
6.1 5
Light Year =
6.1
x ( x 1012 ) km 5 On
6.1 x
9.467
Exp 12 = 4 6 x 6
(-) √ C x ÷ ^
Exp 5 6 7 8 9 + - On 1 2 3 4 . =
Ans = =
x 10
Click after using calculator
Next

49. Light Year Speed of Light is 299 792 458 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 109 km
In 1 year Light travels a distance of km or Million Km or 9.47 x 1012 km
To make sense it may be better to relate this to distances in the Universe

50. One Light Year