 I remember back in the day when I was teaching my sister about decimals I was writing different things like that and asking her to convert between fractions and decimals so 0.29 becomes 29 divided by 100 31 by 100 becomes 0.31 55 by 100 becomes 0.55 and I had written 4 by 100 and she said it's 0.4 and this was not correct 4 parts out of 100 is not 0.4 and rather it is 0.04 let's see why we can understand why 4 parts out of 100 is not 0.4 and rather 0.04 we have to understand this grid here in both the grids I have 100 equal parts let's just assume this is a grid of 100 equal parts and on the right as well there are 100 equal parts and I have shaded 4 parts out of those 100 in green and on the right hand side I have shaded 40 of those 100 parts in green so in this case where we have written 4 parts out of 100 the denominator has to be 100 and therefore after the decimal point we will write 0 and then we will write 4 this translates to 0 divided by 10 plus 4 divided by 100 because this is how we expand the decimal numbers on the right hand side we have 40 parts shaded out of 100 and the denominator is 100 again so after the decimal point I can write 40 and this would mean 40 divided by 100 and because you can add any number of 0s after 4 this also means we can write this as 0.4 and this would mean it is 4 by 10 40 by 100 and 4 by 10 are equivalent fractions and therefore 0.4 is basically 0.40 or 400 or 0.4000 and we can conclude that 0.04 is less than 0.4 quite clearly now let's see how we can compare other decimal numbers I have 2 decimal numbers written here so one of them is 1.092 and other is 2.123 to compare the decimal numbers always first look at the left hand side part of the decimal point so just focus on 1 and focus on 2 here which one is greater because 2 is greater here we can straight away write 2.123 greater than 1.092 irrespective of what is the part on the right hand side of the decimal point because it is always less than 1 but what if the numbers had equal whole part so 1.293 and 1.052 let's see how we can expand this if we compare place values we cannot compare 1 and 1 definitely compare the immediately next digit after the decimal point which is 2 in this case and 0 in this case and because 2 is greater so 2 by 10 is greater than 0 by 10 we can write 1.293 to be greater than 1.052 now what if we wrote 2.352 and on the right hand side we had 2.43 now which one is greater so if you just look at the part on the right after the decimal point in both numbers it just seems like 352 is larger than 43 but we must not forget that we can pad any number of zeros after 43 or after 352 so this is clearly not the right way to compare these 2 decimal numbers what you need to do is to only look at the immediately next number after the decimal point first so here it is 3 and here it is 4 and 4 is larger than 3 so 2.352 is less than 2.43 just to get the idea 2.43 can also be written as 2.430 and on the left hand side you will see 2.352 what if the immediately next number is also same so for example 3.525 and then you have 3.569 now the immediate next number after the decimal point is also equal so you compare the next number or the next digit on the right so here 2 is less than 6 here and so 3.525 is less than 3.569 and this is how we compare decimal numbers