Rational number word problem: computers

in the year 1944 computers weighed as much as 4,500 kilograms a modern laptop weighs around 2.7 kilograms what is the ratio of how much computers weighed in 1944 to how much a modern laptop weighs express your answer as a ratio of two integers so the ratio of how much computers weighed in 1944 so we know that's 4,500 kilograms 4,500 kilograms we want the ratio of that to how much a modern laptop weighs and thats 2.7 kilograms so this right over here is a ratio but we haven't expressed it as a ratio of two integers in particular 4,500 is an integer but 2.7 is not an integer so the easy way to convert 2.7 to an integer is to move the decimal place one to the right or another way of thinking about it is to multiply it by 10 so we could multiply this by 10 but that would if we just multiply the denominator by 10 that would change the value of the ratio in order to not change the value we have to multiply the numerator and the denominator by 10 this is equivalent to just multiplying this fraction by 10 over 10 which is the same thing as 1 does not change the value so what do we get well in the numerator 4500 times 10 is 45,000 put a comma here makes it a little bit easier to read and in the denominator this is the whole point of why we multiplied by 10 to point 7 but multiplied by 10 is 27 so we now have expressed our ratio or we've now expressed our answer as a ratio of two integers so this is completely legitimate but we could also simplify this just looking at this it looks like 45 45,000 is divisible by 45 which is divisible by 9 and 27 is also divisible by 9 so why don't we divide the numerator and the denominator both by 9 and we're going to get so we're going to divide by 9 in the numerator and we're going to divide by 9 in the denominator and we are going to get 45 divided by 9 is 5 so 45,000 divided by 9 is 5000 so we're going to get 5,000 5,000 over 27 divided by 9 is 3 and I think we have now simplified this about as much as we can