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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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Standard form

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

Light Year Intro

Light Year Calculation


How far is it from the earth to the sun

How far is it from the Earth to the Sun

BOOM!

How far?

92 000 000 miles


Some calculations result in very large answers

Happy 70th Birthday!

How many seconds in 70 years?

Some calculations result in very Large answers

SPLAT!

70 years = 2 200 000 000 seconds!


Using millions to understand the size

Using millions to understand the size

Dinosaurs roamed the earth 228 000 000 years ago

Dinosaurs roamed the earth 228 million years ago


Number is different formats

Number is different formats

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


Standard form1

Standard Form

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


Making sense of the code

Making sense of the code

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


Not beginning with 1

6

4

3

2

10

10

10

10

Not beginning with 1

2

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.


Whole no to sf

Whole No to SF

  • 2 000

  • (2) 20 000

  • (3) 500

  • (4) 800 000

  • (5) 9 000 000

= 2 x 10 x 10 x 10

= 2 x 10x10x10x10

= 5 x 10 x 10

= 8x10x10x10x10x10

= 9x10x10x10x10x10x10


43620 to standard form

43620 to STANDARD FORM

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


To change to standard form

To change to STANDARD FORM

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


3820000 to standard form 2

3820000 to STANDARD FORM 2

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


To change to standard form 2

To change to STANDARD FORM 2

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


907 5 to standard form 3

907.5 to STANDARD FORM 3

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


To change to standard form 3

To change to STANDARD FORM 3

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


Large to sf interactive

Large To SF Interactive

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


Large to sf examples

Large to SF Examples

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


12 7 millions to sf

12.7 Millions to SF

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


Millions to sf

Millions to SF

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


Millions to sf examples

Millions to SF : Examples

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


Standard form to normal

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

10

x

1

1

0

0

0

0

0

0

0

0

0

=

Normally the 1st number includes a point.


What is

2

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)


Sf to normal

4

T

SF to Normal

x 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


Back to normal

Back to Normal

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


Back to normal1

Back to Normal

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


Large sf to normal

Large SF to normal

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


Sf to normal examples

SF to Normal Examples

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


Small numbers

Small Numbers

How wide is an atom?

0.000 000 000 1 metres wide!

Small numbers like this will have negative powers of 10


Introducing small

8

T

Introducing Small

x 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


Small to sf

Small to SF

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


Small numbers1

Small Numbers

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


Small numbers2

Small Numbers

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


Small to sf interactive

Small To SF Interactive

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


Small to sf examples

Small to SF Examples

-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


Small sf to normal

4

T

Small SF to Normal

x 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


Small sf to normal1

Small SF to Normal

-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


Small sf to normal2

Small SF to normal

-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


Small sf to normal examples

Small SF to Normal Examples

-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


Positive powers

Positive Powers

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


Negative powers

Negative Powers

-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


Mixed powers

Mixed Powers

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


Light year

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.


Light years

Light Years

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


Distances around the universe

Distances around the Universe

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


Time for light to travel from

Time for light to travel from

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


4 22 light years

12

x 10x

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 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


7 light years

12

x 10x

12

x 10x

7 Light Years

7 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


Light year calculations

Light Year Calculations

1 Light Year is 9.467 x 1012 km

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x ( 9.467 x 1012 ) km

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6.1

Light Year =

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9.467

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Click after using calculator

Next


Light year1

Light Year

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


One light year

One Light Year


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