My daughter has two questions on her homework that we can't figure out. Hopefully someone can help us.
(1)Explain what happens when you round 9,999.999 to any place.
(2)Describe two real-world situations in which it makes sense to round numbers.
My daughter has two questions on her homework that we can't figure out. Hopefully someone can help us.
(1)Explain what happens when you round 9,999.999 to any place.
(2)Describe two real-world situations in which it makes sense to round numbers.
What happens, is that 9 rounds up to 10, but if you did that in any position to the right of the first digit in the number this is what happens:
Let's take your number 9,999.999:
If we round the last digits up to the nearest one, we see that we have the following chain reaction:
$\displaystyle 9,999.9(9+1)0\implies9,999.(9+1)00\implies9,99(9+1 ).000\implies9,9(9+1)0.000$ $\displaystyle \implies9,(9+1)00.000\implies (9+1),000.000\implies 10,000.000$
No matter where you start to round up, you will always end up with $\displaystyle 10,000.000$
I hope this makes sense.
For example, if you measure someone's height. We usually say that someone is 6'1'', 5'7'', 5'10'', etc. Anything we measure is continuous; we can never give an exact value for it. There will always be rounding errors. Also, it wouldn't make sense to say that you're 5'11.1267844568395678923532479234...''(2)Describe two real-world situations in which it makes sense to round numbers.
Another example would be when dealing with money. The number representation of money never exceeds more than 2 decimal points to the right.
For example, we may see that a bottle of soda may be $\displaystyle \$1.25$, but not $\displaystyle \$1.25343$
Hopefully this makes sense!
--Chris
For a great animated/narrated explanation about rounding off decimals that is EASY to understand, check this:
Mathematics.com.au - Rounding Off Decimals