# Write the number 112 in "expanded form."

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(1 * 100) + (1 * 10) + (2 * 1)

Expanded form is a way of writing a number so that you can see how a number is "constructed" out of other numbers. It is sort of like looking under the hood of a number to see what makes it tick.

In your example of 112, we would have 1 X 100 + 1 X 10 + 1 X 2=112 (remember that the multiplication parts of the problem are done before the addition parts according to the order of operations.) If you add those together, you get 112. This is similar to what is called "standard" form, which would be 100+10+2=112.

The number 112 in expanded form would look like :

100 + 10 + 2 = 112

100 + 10 + 2 = 112

112

100+ 10 + 2 = 112

(100*1)+(10*1)+(2*1)

a little simplified is 100+10+1+2

The expanded form in any x ( x is an imteger) base system is like a polynomial in the form:

An*x^n+An-1x^(n-1)+An-2*x^(n-2)+An-3*x^(n-3)+......A2*x^2+A1*x+A0, where An , An-1, An-2, ....A2,A1 and A0 are the positive integral coefficients such that 0 <= Ar< x and r is an integer 1 to n.

You did not cite the base. So, we take first 10 base , the most popular a decimal system and then one hundred and twelve converted in base 5 and its expansion in the powers of 5 and the number 112 in base 5 and its expansion.

Procedure:

(i)

112 in 10 base:

So the 112/10 = quotient 11+**remainder 2.**

Take the quotient 11 above and divide by 10 to get the quotient and remainder:

11/10= quotient 1+** remainder 1**

Take the quotient 1 above and again divide to get quotient and remainder:

1/10 = quotient 0 + **remainder 1**

Procedure is to go till the quotient is 0.

112= 3rd remainder* 10^ (3-1)+(second remainder*10^(2-1)+first remaider*10^(1-1)'

Therefore, 112= 1*10^(3-1)+1*10^(2-1)+2*10^(1-1) or

112=1*10^2+1*10+2*10^0 or

112=1*10^2+1*10^1+2*10^0 0r

112=1*100+1*10+2.

(ii)

112 converted in 5 base:

112/5=quotient 22 +remainder 2

22/5= quotient 4 + remainder 2

4/5= quotient 0 remainder 4

Therefore 112 (one hundred and five) in base 5 = 4*5^2+2*5+2.

(iii)

Now 112 in base 5 = 1*5^2+1*5+2