See full explanation below
Explanation:
First, in order for you to understand this, you need first to understand what is significant figure.
A significant figure of a number are digits that carry meaning contributing to it's measurement resolution. This includes all digits of a number, with the exception of the following cases:
1. All leading zeros, example 0.0016. In this case, you don't count the leading zeros, and the significant figure of this number is 1 and 6, two significant figure
2. trailing zeros but only when they are placeholders to indicate the scale of a number.
Now, you know which cases digits are not significatives, but which are significants? these:
1. All non zero digits.
2. zeros between non zero digits (ex: 605)
Now that we know this, let help you with the question 2.
a) 3427: non zero digits, it has 4 digits, and therefore, 4 significant figure
b) 0.00456: Three leading zero, not counted, so it only has 3 significant figures
c) 123.453: even with the decimals, you count all the non zero digits here. It has 6 significant figure.
d) 172: 3 significant figure.
From here, I'll call significant figure as SF.
e) 0.000984: 3 SF (4 leading zero)
f) 0.502: one leading zero, 3 SF
g) 3100.0 x 10^2: in this case, we have a power of 10. To know this, all you need to do is to run the dot, the spaces that the exponent says; in this case, 10^2, means that you are going to run the dot 2 spaces and in this case to the right; as we do not have another digit, you complete the number adding zeros, so:
310000 this is the real number, but scientific notation, put the number with only one dot, and one zero, so we have only 5 SF. That's because the two zeros after the dot, the last one is a trailing zero, that's why we do not count it.
h) 0.0114 x 10^4: leading zeros not counted, 3 SF
i) 107.2 : 4 SF
j) 0.0000455: 3 SF
k) 2205.2: 5 SF
l) 30.0 x 10^-2: when the exponent is negative, we run the dot to the left and add zero if it's neccesary. In this case, it would be 0.300, leading zero not counted, 3 SF.
m) 0.982 x 10^-3: leading zeros no, 3 SF
n) 0.0475: 3 SF
o) 650.502: 6 SF
p) 3.03 x 10^-1 = 0.303 = 3 SF
q) 20.4 x 10^5 = 2040000 = trailing zero, 3 SF
r) 1.29: 3 SF
s)0.00565: 3 SF
t) 1362205.2 = 8 SF
u) 450.0 x 10^3: 4 SF (the other zeros to the right are trailing zeros)
v) 1000 x 10^-3 = 1 = 1 SF
w) 546,000 ± 10: in this case, we have a range of error, which is 10, so we can either sum 10 or take out ten to this number. This number could be 546,010 or 545,990. In either way we have the same SF, ans in this case it would be 6 SF.
x) 546,000 ± 1000 = same as above, but the range is wider, it could be 545000 or 547000. 6 SF.
Now for question 3, as I said above, you should run the dot the number of time the exponent says to the right (If exponent is positive and add zero when it's needed) or to the left (if exponent is negative and add zero when it's needed):
1.56 x10^4 = 15,600
0.56x10^-2 = 0.0056
3.69x10^-2 = 0.0369
736.9x10^5 = 73690000
0.00259x10^5 = 259
0.000459x10^-1 = 0.0000459
13.69x10^-2 = 0.1369
6.9x10^4 = 69000
0.00259x10^3 = 2.59
0.0209x10^-3 = 0.0000209
