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1. The population of a town is 680 000 correct to the nearest 10 000. Write down
(i) the least possible population of the town
(ii) the greatest possible population of the town
2. Light travels 1 metre in 3.34 nanoseconds.
Find the distance, in kilometres, light travels in one second. Give your answer in standard form.
3. Given that 3 < x < 7 and -2 < y < 5, find
(a) the smallest value of xy
(b) the smallest value of y^2
"The population of a town is 680 000 correct to the nearest 10 000."
The population might be as low as 679,000 or as high as 681,000.
Go to physics.nist.gov/cuu/Units/prefixes.html
You just have to memorize this stuff, at least the ones you work with all the time. It's ok to bookmark the page so you can look up the others when you run across them.
There is a prefix every three powers of ten, except for 100, 10, 1/10, and 1/100. To go from one to another you use the LARD rule: LEFT ADD RIGHT DEDUCT. When moving the decimal to the LEFT you ADD to the power of ten. When going to the RIGHT you DEDUCT from the power of ten.
"Nano" means 10^-9 so "1 metre in 3.34 nanoseconds" can be written as m/3.34 x 10^-9s or 3.34 x 10^-9s/m whichever works in your equation. The assignment is "Convert 1m/3.34 x 10^-9s to km/s." A conversion factor is a fraction equal to 1. You are given that one hour equals 60 minutes so you can write that as hr/60min=1 or 60min/hr=1 whichever works for you and drop it into an equation anywhere and it only changes the units.
ANSWER = You write this first so it looks like you know what you are doing. That gives you a bit of time to figure out what to do next.
ANSWER = m/3.34 x 10^-9s x km/1000m
Ok, now we check everything. This is called sanity check and it is especially important in chemistry and physics where you might have a dozen or so conversions in a single equation. We have m on top of the fraction line and again below so that cancels. We have s below the line and that appears in the answer just like we want it. We have km above the line and that appears in the answer just like we want it. When you are sure everything is right, multiply all the numbers above the line and divide by all the numbers below the line.
ANSWER = m/3.34 x 10^-9s x km/1000m = 299.4011976 x 10^3 km/s
Standard form is whatever your teacher says it is. You would use the LARD rule to convert that to 299,401.1976 km/s.
