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let's compare zero point one to zero point zero seven zero so this one right over here it is in the tenths place so it literally represents 1 times 1/10 1 times 1/10 which is obviously the same thing as 1/10 now when we look at this number right over here it has nothing in the tenths place it has seven in the hundredths place so this is the hundreds place right over here and then it also has nothing in the thousandths place so this number can be rewritten as seven times as seven times one over 100 or seven hundredths seven hundredths and now we could compare these two numbers and there's two ways you could think about it you could try to turn one tenth into hundredths and the best way to do that if you want the denominator be increased by a factor of ten you need to do the same thing to the numerator so all I did is I multiplied the numerator and denominator by ten ten 100's is the exact same thing as 1/10 and here it becomes very clear ten hundredths is definitely larger than seven hundredths another way you could think about this is look if you were to increment by hundreds here you would go to seven hundred or you start at seven hundred eight hundredths nine hundredths and then you'd get to ten hundredths so then you would get to that number so this number multiple ways you could think about it is definitely larger so let me write this down this is definitely larger greater than this is greater than that I the greater than symbol opens to the larger value so here we have zero point zero nine three and here we have zero point zero one so let's just think about this a little bit so this nine get a new color here this nine is not in the tenths the hundredths it's in the thousandths place it's in the thousands place and this 3 this 3 is in the I'm running out of colors again this 3 is in the ten thousandths place so the 3 is in the ten thousands place so you could literally view this as nine thousandths nine thousandths +3 ten thousandths three 10,000th and if you just wanted to write it in terms of ten thousands you can multiply the nine and a thousand by zero and so it becomes 90 over ten-thousand I need n thousandths and if you want to add them together you could of course write this as 93 ten thousandth 93 ten thousandths ten-thousandths I always have trouble with that th S at the end now let's think about this number right over here 0.01 well this one right over here is in the hundredths place it's in the hundreds place so it literally represents one hundredth so how can we compare 100 to ninety three ten thousandths so the best way to think about is well what's one hundredth in terms of ten thousandths well let's just multiply both the numerator and the denominator here by 10 twice or you could say let's multiply them both by hundred so if you multiply by 10 once you get to ten thousandths is the same thing as 100 multiplied by 10 again you get a hundred ten thousands is the same thing as 100 then we know that 100 times 100 is 10,000 so here it becomes very clear 110 thousandths or one hundredths is definitely larger than 93 ten thousandths so this quantity right over here is less than this quantity they're less than symbol the small end points to the smaller number larger n to the larger number in fact that's true of the less-than and greater-than so let's see this one right over here zero point six versus 0.06 so here I have a six in the tenths place so it literally represents six tenths and here and in the second around was six in the hundredths place well the hundred six hundredths is definitely smaller than six tenths 1/100 is a tenth of a tenth so this this one is pretty straightforward this is going to be the larger value zero point six is greater than zero point zero six now let's think about zero point three versus zero point zero six so this three literally represents three tenths three tenths well this six right over here well this six right over here represents six hundredths six hundredths and if you wanted to compare them directly you can multiply three tenths times well then both the numerator and the denominator by 10 so you're not changing its value 10 over 10 is essentially 1 or it is 1 so this becomes 30 over 300 3/10 is the same thing as 30 over 130 over 100 is a lot larger than 6 over 100 so this is greater than