Question

Hello, can you explain this topic im in 6th grade ​

Answer 1

Hello there I hope you are having a great day :)

The Topic Shifting digits:

Shifting digits - Putting a digit in a different place. For a example Take the number 358 you would exchange the number from the hundreds that would equal 838 this meaning that you what to make a bigger number than a small one.

Examples:

1. 358 equal 838

2. 204 equal 402

3. 188 equal 881

You are just making them smaller to a greater number :)

Hopefully that helps you :)

 

Answer 2

Step-by-step explanation:

this is to make you aware what "power" or "value" is associated with what position in a number.

when I write a number like in the example above

795

then the strongest, most powerful value in the whole number is with the digit in the outmost left position.

the second most powerful with the digit in the next position to the right. and sin on.

and the digit in the outmost right position has the least value.

to make sure that there is no overlap between the positions, every position corresponds to a certain power of 10 level. each position to the left is one level higher, and another level higher and so on.

as we start with 10⁰, the levels go up to number of positions - 1.

3 positions means we go up to 10².

795 = 7×10² + 9×10¹ + 5×10⁰

or

42186 = 4×10⁴ + 2×10³ + 1×10² + 8×10¹ + 6×10⁰

by the way, you know that x⁰ = 1 for any value of x.

if we go into the decimals, then the same principle applies also on the right side of the decimal point. each position further right decreases the exponent of 10 by 1.

23.073 = 2×10¹ + 3×10⁰ + 0×10^-1 + 7×10^-2 + 3×10^-3

it is very important when handling and calculating numbers to stay always very aware of the positions the digits have in the actual number(s). and to combine always only the digits in the right corresponding positions for calculations or comparisons.

bottom line of this exercise above is therefore, if you put a smaller digit into the first position (outmost left), then the number value gets smaller, no matter what you do with the remaining digits in their positions.

and the other way around (bigger digit in the first position makes the number value bigger). it gets smaller or bigger with the associated power of 10.

you can imagine these associated powers of 10 as proponents or "bullies" of the corresponding digits. the bigger the exponent of 10, the stronger and effective the "bully".

on the other end :

even if you put a 9 instead of a 0 into the last (outmost right) position, the number value gets a little bit bigger. it has only the weakest "bully" to "make it heard". it only makes a difference, if the other digits are the same.

e.g.

52760 is smaller than 52769.

but

52770 is bigger than 5276x, no matter what digit you put in for x.

this is what this exercise tries to show you, and the playing around with the numbers should create a "feeling" in you to always think about it, even if it is only sub-consciously.