Explain how the cartons and boxes for table tennis balls are like the digits for numbers in our base-10 number system.

Base 10 Number System = (0,1,2,3,4,5,6,7,8,9)

In a  Carton of table tennis there are  10 boxes.

And Each Box can Hold 10 Balls.and if i mark boxes from 0 to 9, then

then there are 10 boxes , Total number of Balls=100

So if I represent a single Carton by A, then

A[single carton] ={0,1,2,3,4,5,6,7,8,9}= 10 boxes =100 balls

B [2 carton]= 20 boxes=200 balls

C[ 5 cartons + 3 Boxes] = 5× 100+ 3×10 =530 balls

D[ 12 cartons + 8 Boxes]= 12×100+8×10=1280 balls

Now you can see,

Each carton is holding the balls  in decimal number system.

Boxes = Ten's place in number system,

Number of cartons = either Hundred place or thousand place or more than that

In this way we can represent Carton and Box for table tennis balls in decimal number system having base 10 .

To explain the cartoons and the boxes for table tennis balls are like the digits for numbers in base-10 number system

Here we know that, the number of table tennis balls in one box =10 balls

and the number of table tennis balls in boxes in each cartoon = 10 balls

Therefore, The number of table tennis balls in each cartoon =10×10=100 balls

Hence for the number of balls ,the hundreds place tells the number of cartoons and  tens place tells the number of boxes which left as remainder or without cartoon.

For example if the total tennis balls =540 then its hundreds place i.e 5 tells the number of cartoons and its tens place i.e.4 tells the number of boxes which left as remainder or without cartoon.