Basic Math University

[jennygore1977]

I was wondering if you could tell if I got this math problem right 0.727 * 3.5
The answer i got was 2.5445. please and thank you

 

[JeffM]

I was wondering if you could tell if I got this math problem right 0.727 * 3.5
The answer i got was 2.5445. please and thank you

You can always check your own work on a calculator (except maybe on tests). Because I am bone lazy, it's what I did to confirm that you got the right answer. I get that they want you to understand how to do these computations. People use calculators incorrectly every day, and you are less likely to do that if you understand what the calculator should be doing.

If you know scientific notation, you can easily check without a calculator that your answer is is approximately right by doing a simpler but closely related problem.

\(\displaystyle 3.5 * 0.727 \approx 3.5 * 0.7 = 3.5 * 10^0 * 7 * 10^{-1} = 24.5 * 10^{-1} = 2.45 \approx 2.5445\)

 

[jennygore1977]

Thank you

Thank you so much

 

[HallsofIvy]

Another way to look at is that 3.5*.727= (3+ .5)(.727)= 3(.727)+ .5(.727).

.5= 1/2 of course so that last is .727/2. 2 divides into 7 3 times with remainder 1. 2 divides into 12 (the "2" in .727 together with the remainder from the first division) 6 times with no remainder. So far we have '.36'. 2 divides into that last 7 three times with remainder 1 again and then 2 divides into 10 (the remainder 1 together with 0 since there is no further digit) 5 times. That is .5(.727)= .3635.

To multiply 3 times .727, 3 times the last 7 is 21 so the last digit will be 1 and we "carry" the 2. 3 times the 2 in .727 is 6 and then we add the 2 we carried to get 8. 3 times the very first 7 is again 21 so, without the decimal that would be "2181". Since the original .727 had three decimal place and 3 had none, the result has three decimal places: 2.181. As a check, 3 times .7 is 2.1 so 3 times .727 must be close to that.

Finally, 3.5*.727= 3(.727)+ .5(.727)= 2.181+ .3635. To add that, rewrite as 2.1810+ 0.3635 so the decimal places match up. 0+ 5= 5 so the last digit is 5. 1+ 3 is 4 so the next digit is 4. 8+ 6= 14 so the next digit is 4 and we "carry" 1. 1+ 3 is 4 and the "carried" 1 gives 5 so the next digit is 5. Finally, 2+ 0= 2 so the digit outside the decimal place is 2: 2.5445.