# Math Help - explain decimal system urgently

1. ## explain decimal system urgently

hello friends,

My teacher said, in decimal system, Each digit appearing to the left of the decimal point represents a value between zero and nine times an increasing power of ten. Digits appearing to the right of the decimal point represent a value between zero and nine times an increasing negative power of ten.

Could anyone explain to me this paragraph?

2. Originally Posted by learning_maths
hello friends,

My teacher said, in decimal system, Each digit appearing to the left of the decimal point represents a value between zero and nine times an increasing power of ten. Digits appearing to the right of the decimal point represent a value between zero and nine times an increasing negative power of ten.

Could anyone explain to me this paragraph?
take 123.456

the 1 is in the hundreds position, so it is expressed as 1 x 10^2

for the 2, it is 2 x 10^1

the 3, it is 3 x 10^0

the 4, it is 4 x 10^{-1}

the 5 is 5 x 10^{-2}

the 6 is 6 x 10^{-3}

that's all you teacher was saying and obviously this is true. if you sum all the things i gave you together you get 123.456

3. What this means is that I can write a number as the sum of powers of ten times positive integer numbers less than 10. Perhaps the best way to understand this is to do some examples.

example 1:
$4329 = 4000 + 300 + 20 + 9 = 4(10^3) + 3(10^2) + 2(10^1) + 9(10^0)$

The whole number 4329 is really the sum of integers less than 10 times powers of ten.

example 2:
$16.432 = 10 + 6 + .4 + .03 + .002 = 1(10^1) + 6(10^0) + 4(10^{-1}) + 3(10^{-2}) + 2(10^{-3})$

This is what is called writing in the base 10 numbering system.

4. Thank you friends.
Very nice explanation.
Now I got it. Really it is amazing forum. I think now I can get full marks in Maths.

Although I understand what exactly my teacher wanted to say, I have one more doubt friend.

what exactly (between zero and nine times an increasing power of ten) means?????

actually what the word "times" means here? Is it multiply?