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. 0.0005362. Small SF to normal.
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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
0.0005362
Small SF to normal
Light Year Intro
Light Year Calculation
Happy 70th Birthday!
How many seconds in 70 years?
Some calculations result in very Large answersSPLAT!
70 years = 2 200 000 000 seconds!
Dinosaurs roamed the earth 228 000 000 years ago
Dinosaurs roamed the earth 228 million years ago
CostSavers made a profit of £7 500 000
MegaSales made a profit of £ 1 230 000
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
A number in STANDARD FORM has two parts
7
x
10
1.01
1.01
12
x
10
1.01
5.038
8
x
10
1.01
2.79
18
x
10
1.01
9.999
Number between 1 and 9.999999999….
x
Power of 10
10
100 = 10 x 10
1 000 = 10 x 10 x 10
10 000 = 10 x 10 x 10 x 10
100 000 = 10 x 10 x 10 x 10 x 10
1 000 000 = 10 x 10 x 10 x 10 x 10 x 10
4
3
2
10
10
10
10
Not beginning with 12
x
=
200 = 2 x 10 x 10
x
4
=
4 000 = 4 x 10 x 10 x 10
x
7
=
70 000 = 7 x 10 x 10 x 10 x 10
x
3
=
3 000 000 = 3 x 10 x 10 x 10 x 10 x 10 x 10
This is also known as
Scientific Notation.
= 2 x 10 x 10 x 10
= 2 x 10x10x10x10
= 5 x 10 x 10
= 8x10x10x10x10x10
= 9x10x10x10x10x10x10
4
3
6
2
0
10
4
3
6
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
4
3
6
2
0
4
3
2
1
10
4
3
6
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 10
0
0
3
8
2
0
0
x
10
3
8
2
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
0
0
3
8
2
0
0
6
5
4
3
2
1
10
3
8
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 10
9
0
7
5
x
10
5
9
0
7
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
9
0
7
5
2
1
5
10
9
0
7
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
2
907.5 = 9.075 x 10
5
0
0
0
0
0
0
8
9
1
0
0
0
0
5
10
x
4
6
6
x
0
New Example
Test
x
÷
^
Exp
()
√
C
²
7.53x10^5
On
+

5
6
7
8
9
753000
.
=
0
1
2
3
4
Ans
4
x
10
5.27
(a)
52700
6
5
0
0
0
0
0
0
0
0
0
0
5
x
10
6.65
(b)
6650000
8
x
10
2.4
(c)
240000000
4
6
6
6
x
6890000
x
10
6.89
(d)
3
4510
x
10
(e)
4.51
5
805000
x
10
8.05
(f)
x
÷
^
Exp
()
√
C
²
7.84x10^6
New
On
+

5
6
7
8
9
7840000
.
=
0
1
2
3
4
Ans
Change 12.7 million to Standard Form
0
0
0
0
0
1
2
7
6
7
5
4
3
1
2
x
10
1
2
7
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
7¾ million = 7.75 million
Change 7¾ million to Standard Form
0
0
0
0
7
7
5
6
5
4
3
1
2
x
10
7
7
5
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
6
x
10
(a)
5.3
5.3 million
6
5
0
0
0
0
0
0
0
0
0
0
5
x
10
1.3
(b)
1.3 million
7
49 million
x
10
4.9
(c)
4
6
6
x
7
78 million
(d)
x
10
7.8
6
7 million
(e)
x
10
7
7
16 million
1.6
(f)
x
10
x
÷
^
Exp
()
√
C
²
New
On
+

5
6
7
8
9
0
.
=
0
1
2
3
4
Ans
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
10
x
1
1
0
0
0
0
0
0
0
0
0
=
Normally the 1st number includes a point.
3
3
8
6
5
3 x 10
6 x 10
7 x 10
9 x 10
8 x 10
4 x 10
What is …… ?= 600
(1)
= 8 000
(2)
= 400 000
(3)
= 700
(4)
= 300 000 000
(5)
= 9 000 000
(6)
T
SF to Normalx 10
.
5
1
7
3
1
3
7
.
1
5
3
3
3
3
3
0
3.715x10
=
2
3.715x10
=
3
7
1
.
5
9
9
9
9
9
0
3
3
7
1
5
.
6
0
0
0
0
0
3.715x10
=
4
3
7
1
5
0
.
0
0
0
0
0
3.715x10
=
5
7
2
1
8
0
0
.
6
6
0
0
7.218x10
=
6
.
7
2
1
8
0
0
0
6
6
0
7.218x10
=
7
7
2
1
8
0
0
0
0
.
6
0
7.218x10
=
8
7
2
1
8
0
0
0
0
0
.
0
7.218x10
=
4
7
1
5
3
0
0
0
0
0
3.715 x 10
Multiplying by a +ve power of 10 moves the point to the right
Finish
Next
7
10
x
4
3
6
2
0
0
0
0
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
2
10
x
5
0
8
4
4
5
0
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
6
10
3
8
6
4
x
5
0
0
0
0
0
3
6
0
0
0
0
5
4
6
6
x
0
New Example
Test
Place Point
x
÷
^
Exp
()
√
C
²
6
On
+

5
6
7
8
9
0
.
=
0
1
2
3
4
Ans
3
4730
x
10
(a)
4.73
3
5
0
0
0
0
0
0
0
0
0
0
5
9620
x
10
(b)
9.62
5
647000
x
10
(c)
6.47
4
5
6
6
x
873000
x
10
8.73
(d)
3
3160
(e)
x
10
3.16
5
277000
x
10
2.77
(f)
x
÷
^
Exp
()
√
C
²
7.84x10^6
New
On
+

5
6
7
8
9
7840000
.
=
0
1
2
3
4
Ans
How wide is an atom?
0.000 000 000 1 metres wide!
Small numbers like this will have negative powers of 10
T
Introducing Smallx 10
.
9
3
3
0
0
7
6
3
9
0
0
_
_
.
3.9x10
=
2
.
3.9x10
=
0
0
0
6
3
9
0
7
_
_
1
.
0
0
0
0
3
9
5
7
_
_
3.9x10
=
0
0
0
0
0
3
.
9
5
7
_
_
3.9x10
=
1
0
0
0
0
.
3
9
5
7
_
_
3.9x10
=
2
0
0
0
0
3
9
5
7
_
_
.
3.9x10
=
3
0
0
.
0
0
3
9
5
7
_
_
3.9x10
=
4
.
0
0
0
0
3
9
5
7
0
_
3.9x10
=
8
1
0
0
3
0
0
0
0
Number >=1 …….. Power of 10 will be positive
0
3.9 x 10
Number between 0 and 1 …….. Power of 10 will be negative
Next
0.0000194
0.00132
0.0000042
0.15
0.0000042
0.0000846
0.39
=
6
4.42
x
10
0.97
0.0000035
0.012
0.0596
0.00007
0.1
Click number to convert. Numbers from 0 to 1 have negative powers. Compare number of zeros at front to the power.
Next Examples
0
0
0
0
5
3
6
2
2
3
4
1
10
3
6
2
5
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
4
0.0005362 = 5.363 x 10
0
7
8
1
1
10
x
8
1
7
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
5
0
0
0
0
0
0
8
7
9
5
0
0
0
5
10
x
4
6
6
x
Click top no then click destination.
Use arrows to set power
0
New Example
x
÷
^
Exp
()
√
C
²
Test
On
+

5
6
7
8
9
0
.
=
0
1
2
3
4
Ans
6
x
10
(a)
1.42
0.00000142
3
5
0
0
0
0
0
0
0
0
0
0
5
x
10
6.27
(b)
0.00627
4
0.00075
x
10
7.5
(c)
4
6
6
x
3
0.0012
(d)
x
10
1.2
3
0.00933
(e)
x
10
9.33
8
0.0000000388
3.88
(f)
x
10
x
÷
^
Exp
()
√
C
²
New
On
+

5
6
7
8
9
0
.
=
0
1
2
3
4
Ans
T
Small SF to Normalx 10
.
7
3
4
8
3
0
0
7
6
8
4
3
7
_
_
.
8.437x10
=
2
.
8.437x10
=
0
0
0
6
8
4
3
7
_
_
1
.
0
0
0
0
8
4
3
7
_
_
8.437x10
=
0
0
0
0
0
8
.
4
3
7
_
_
8.437x10
=
1
0
0
0
0
.
8
4
3
7
_
_
8.437x10
=
2
0
0
0
0
8
4
3
7
_
_
.
8.437x10
=
3
0
0
.
0
0
8
4
3
7
_
_
8.437x10
=
4
.
0
0
0
0
8
4
3
7
0
_
8.437x10
=
4
When the power is negative the point moves to left
1
0
0
8
0
0
0
0
0
8.437 x 10
There will be the same no of zeros at front as power
Next
8
10
x
7
8
0
3
0
7
8
0
3
0
0
0
0
0
0
0
=
0
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
6
10
2
8
5
1
x
5
0
0
0
0
0
7
5
1
0
0
0
5
4
6
6
x
0
New Example
Test
Place Point
x
÷
^
Exp
()
√
C
²
6
On
+

5
6
7
8
9
0
.
=
0
1
2
3
4
Ans
5
0.0000742
x
10
(a)
7.42
5
5
0
0
0
0
0
0
0
0
0
0
5
0.0000701
x
10
(b)
7.01
8
0.0000000103
x
10
(c)
1.03
4
6
6
x
6
0.00000321
(d)
x
10
3.21
4
0.000891
(e)
x
10
8.91
4
0.000238
2.38
(f)
x
10
x
÷
^
Exp
()
√
C
²
New
On
+

5
6
7
8
9
0
.
=
0
1
2
3
4
Ans
6
1200000
x
10
(a)
1.2
5
5
0
0
0
0
0
0
0
0
0
0
5
924000
x
10
(b)
9.24
6
7100000
x
10
(c)
7.1
4
6
5
6
x
562000
x
10
5.62
(d)
5
418000
x
10
4.18
(e)
3
3420
x
10
3.42
(f)
x
÷
^
Exp
()
√
C
²
7.84x10^6
New
On
+

5
6
7
8
9
7840000
.
=
0
1
2
3
4
Ans
5
0.0000782
x
10
(a)
7.82
5
5
0
0
0
0
0
0
0
0
0
0
5
0.0000658
x
10
(b)
6.58
4
0.000543
x
10
(c)
5.43
4
6
8
6
x
0.0000000913
x
10
9.13
(d)
3
0.00206
x
10
2.06
(e)
6
0.00000239
x
10
2.39
(f)
x
÷
^
Exp
()
√
C
²
7.84x10^6
New
On
+

5
6
7
8
9
7840000
.
=
0
1
2
3
4
Ans
4
73600
x
10
(a)
7.36
3
5
0
0
0
0
0
0
0
0
0
0
5
0.00884
x
10
(b)
8.84
8
649000000
x
10
(c)
6.49
4
6
3
6
x
5280
x
10
5.28
(d)
6
8000000
x
10
8
(e)
4
3.11
0.000311
x
10
(f)
x
÷
^
Exp
()
√
C
²
7.84x10^6
New
On
+

5
6
7
8
9
7840000
.
=
0
1
2
3
4
Ans
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.
Distances in the solar system are vast.
Distance from the Sun to Pluto is
59 400 000 000 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 22 000 times the time so about 22000 the distance
The distance from the Sun to the Earth is
150 000 000 km or 1.5 x 108 km
It is hard to make sense of this distance
The distance round the equator is about 38 000 km or 380 hours (nearly 16 days ) by car.
The distance from Sun to Earth is about 4 000 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
8 min 20 sec
Earth to the Sun
5 min 10 sec
Earth to Mercury
2 min 20 sec
Earth to Venus
1.268 sec
Earth to the moon
4 min 10 sec
Earth to Mars
35 min
Earth to Jupiter
71 min
Earth to Saturn
2 hr 31 min
Earth to Uranus
4 hrs 2 min
Earth to Pluto
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 3 600 RETURN journeys to the moon
x 10x
4.22 Light YearsProxima 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 9.467 x 1012 km
Distance to Proxima Centauri is 4.22 Light Year
Light Year
9.467 x 1012 km
4.22
4.22x9.47 x 1012 =
4.22 x 9.47
E
12
4.22 x
4.22 x 9.467
=3.995 x 1013 km
x 10x
12
x 10x
7 Light Years7 Light Year
Light Year
9.467 x 1012 km
7
7x9.47 x 1012 =
7 x 9.47
E
12
7 x
7 x 9.467
=6.629 x 1013 km
32 Light Year
Light Year
9.467 x 1012 km
32
32x9.47 x 1012 =
32 x 9.47
E
12
32 x
32 x 9.467
=3.0304 x 1014 km
1 Light Year is 9.467 x 1012 km
5
0
0
0
0
0
0
0
0
0
0
5
x ( 9.467 x 1012 ) km
6.1
6.1
Light Year =
=
6.1
12
x
9.467
Exp
On
4
6
6
x
x
÷
^
Exp
()
√
C
²
On
+

5
6
7
8
9
0
.
=
0
1
2
3
4
Ans
=
=
x 10
Click after using calculator
Next
Speed of Light is 299 792 458 m/s
In 1 second Light travels a distance of 300 million metres or 300 000 km
In 1 hour Light travels a distance of 1 080 000 000 km or 1 080 Million Km or 1.08 x 109 km
In 1 year Light travels a distance of 9 467 280 000 000 km or 1 080 Million Km or 9.47 x 1012 km
To make sense it may be better to relate this to distances in the Universe