# Upper and lower bounds

• Mar 24th 2011, 08:10 AM
yorkey
Upper and lower bounds
Hi

Can I please get some clarification on upper and lower bounds.
If the questions asks for the upper and lower bounds of 50 to the nearest centimetre, the answer would be 49.5 and 50.5, right?
And if the question asks for the upper and lower bounds to the nearest 100, then the answer would be 0 and 100.

So what I'm trying to ask is, if the question asks for the nearest 10cm, that there are 10 cm between the two bounds?
Thanks!
• Mar 24th 2011, 07:01 PM
Sambit
Quote:

If the questions asks for the upper and lower bounds of 50 to the nearest centimetre, the answer would be 49.5 and 50.5, right?
What is the "unit" of 50?
• Mar 25th 2011, 02:06 AM
yorkey
Cm.
• Mar 25th 2011, 03:36 AM
HallsofIvy
I think what you are asking for the largest and smallest a measurement could be in terms of the significant figueres given. That is, if the measurement were given as 55 cm., then the "least signifcant figure" is that last 5- the measurement is to the nearest cm, so the true value could be anywhere between 54.5 and 55.5 cm.

But "trailing 0"s are a problem for "significant figures". Trailing 0s may be "significant" or they may just be "place holders". If that 0 is significant, the measurement is again to the nearest cm, so the true value could be anywhere between 49.5 cm and 50.5 cm. But if it is not, then the measurement is to the nearest 10 cm and the true value could be anywhere between 45 cm and 55 cm.

That is why "significant figures" are almost always paired with "scientific notation". If we were given " $5.0 \times 10^1$ cm", or " $5 \times 10^1$ cm" we would know that the "0" in the first is significant simply because it is written. That is, " $5.0 \times 10^1$ cm" has two significant figures and would be anywhere between 49.5 cm and 50.5 cm but that " $5 \times 10^1$ cm" has only one significnt figure and could be anywhere between 45 and 55 cm.