Step-by-step explanation:
you don't understand what the multiplication or division with 10 (or a higher power of 10) does ?
or you don't know. what 10² means ?
this means 10 to the power of 2 or 10 squared and is simply 10 multiplied with itself 2 times : 10×10.
and 10×10 is ... 100.
as you can imagine, this is not restricted to the number 2 (and 10). "power of" can be any number and just indicates how often the base number is multiplied with itself.
a surcharge case is "power of 0", which is simply 1.
now that we understand that, let's have a quick look at how the numbers we are dealing with (in daily life as well as in class and in science) are actually built :
when I write e.g the number
1234
then this actually means
4×10⁰ + 3×10¹ + 2×10² + 1×10³
when I multiply this now by e.g. 10 this becomes
4×10⁰×10 + 3×10¹×10 + 2×10²×10 + 1×10³×10 =
4×10¹ + 3×10² + 2×10³ + 1×10⁴
as you can see, the previous "single" position 4 now becomes a 40.
and the result looks in short form :
12340
so, a multiplication by 10 adds a 0 at the low end of the number.
a multiplication by 10² or 100 (= 10×10) adds then 2 0s at the low end. and so forth.
a division by 10 does the opposite and removes a 0 at the low end of the number.
but what if we don't have any 0 at this position of the number ? then we enter the system of the decimal point.
because on the right side of the decimal point we continue to countdown the exponent of 10 below 0.
the first position right of the decimal point stands for 10^‐1, the second position for 10^‐2, and so forth. and that is nothing else than tenths, hundredths, thousandths, ...
so, in short, a multiplication by 10 moves the decimal point one position to the right. and if we run out of written positions, then we can simply assume an infinite sequence of 0s continuing further to the right.
and a division by 10 moves the decimal point one position to the left. and if we run out of written positions, then we can simply assume an infinite sequence of 0s continuing further to the left too that are then showing up on the right side of the decimal point.
now, I think we covered all the basics and we can look at the question here :
10² × 18.72
10² = 100 = 10×10
so, we are multiplying twice by 10 and move the decimal point therefore 2 positions to the right.
the result is then
1872
as a little guide : when it is clear that the number has to get bigger by the operation (like a multiplication by 10 or 100), you need to move the decimal point in the direction that makes the number bigger (which is to the right).
and if the operation is clearly trying to make the number smaller, then you have to move the decimal point in the direction to make the number smaller (to the left).
