Maths Homework ! Help ..... Powers of 10 ..... need help urgently!?

Question

My daughter recently got some maths homework on the powers of 10 Please help !This is a passage on the worksheet:
In the margin is a list of English number names together with the numbers that they represent. The old meanings were widely accepted until 20 or so years ago: thses old meanings are still standard in some languages ( such as German). In the English speaking world the old usage has been largekly replaces by the new. Only the first three names are widely used.

The Questions:
1. If you know the power of 10 for a number in the new system. how do you work out the power of 10 for the number with the same name in the old system?
2.Each number name has a different prefi. What patterns or rules can you find to help work out which power of 10 is represented by each number.
@- In the old system ?
@- In the new system?

a- How are the powers of 10 related to the prefixes in the old system?
b- How are the powers of 10 related to the prefixes in the new system?
Please help!

This is the table:
Name Old New
Million 10^6 10^6
Billion 10^12 10^9
Trillion 10^18 10^12
Quadrillion 10^24 10^15
Quintillion 10^30 10^18
Sextillion 10^36 10^ 21
Septillion 10^ 42 10^24
Octillion 10^48 10^27
Nonillion 10^ 54 10^30
Decillion 10^60 10^33
Undecillion 10^66 10^36
Duodecillion 10^72 10^39
Tredecillion 10^78 10^42
Quattuordecillion 10^84 10^45
Quindecillion 10^90 10^48
Sexdecillion 10^96 10^51
Septendecillion 10^102 10^54
Octodecillion 10^108 10^57
Novemdecillion 10^114 10^60
Vigintillion 10^120 10^63

This is the table on the sheet.

Answer 1

The you work it out thus:

0.1 = 10 minus 1
0.01 = 10 minus 2
0.001 = 10 minus 3
1=
10 = 10 plus 1
100 = 10 plus 2
1000 =10 plus 3

Answer 2

This seems to be a discussion of the long and short scales. There's a good wikipedia article on it here:
http://en.wikipedia.org/wiki/Long_and_short_scales

The old system she's referring to is the long scale. The meanings for thousand and million are the same, however after that the scales differ - the long scale billion is 10^6 times one million, whereas the short scale billion is only 10^3 times one million. If any number of the form million, billion, trillion, quadrillion, etc. represents 10^n on the short scale, then the corresponding name on the long scale is 10^(2n-6). The second question is more than adequately answered in the wikipedia article, under the heading "comparison"

Answer 3

Move the decimal point to the right of the number 1 Count the number of moves made and prefix it with a negative symbol - This will give the number you quote as a power of 10 Thus: 0.000001 = 10 to the power -6 or 10^ -6 0,0000001 = 10^ -7 10^ -6 10^ -7 is how it should be written.

Answer 4

Are you refering to the engineering. system versus the straight power of 10 system?

If you are refering to the engr. is in multipules of three on your exponent: such as:
1,000 is going to be equal to 1,00 x 10^3 or in engr. it will be 1K
where the K means Kilo or 1,000.

1,000,000 is going to equal to 1.00 x 10^6 or in engr it will be 1M
where the M mean mega or 1,000,000

1,000,000,000 is going to equal to 1.00 x 10^9 or in engr it will be 1G where the G means giga or 1,000,000,000

going the other way into fractions or decimals:

0.001 is going to equal to 1.00 x.10^-3 or in engr it will be 1m where the m means milli or thousandth and it is a lower case letter. remember all decimals are lower case:

0.000001 is going to equal to 1.00 x 10^-6 or in engr, it will be 1u where u means micro or millionths.

0.000000001 is going to equal to 1.00 x 10^-9 or in engr, it will be see as 1n where the n means nano or thousandth of a millionth

0.000000000001 is going to equal to 1.00 x 10^-12 or in engr. it will be seen as 1p where the p means pico or a millionth of a millionth

I can't get greek alpabet on this thing but on the decimal they are in the greek alpahet and this is as close as I can come using standard English characters:

Also you will find this but rarely. You will see there terms deci and centi.

10 is equal to 1.00 x 10^1 or 1D which means 1deci
and
100 is equal to 1.00 x 10^2 or 1C which means 1centi

Hope that helped you out a little.

Answer 5

more info. What old system? What numbers?
Roman Numerals?

Answer 6

I taught maths for a few year but this is incomprehensible
to me.

Answer 7

can you give some additional details?