Answer:
8,040
0.0300
699.5
2.000 x 102
0.90100
90, 100
4.7 x 10-8
10,800,000.0
3.01 x 1021
0.000410
Explanation:
First remember the following rules of determining the last significant place value :
1. The digits from 1-9 are all significant and zeros between significant digits are also significant.
2. The trailing or ending zeroes are significant only in case of a decimal number otherwise they are ignored. However starting zeroes of such a number are not significant.
Now observing above rules, lets determine the location of the last significant place value of each given example. I am determining the location by turning the last significant place to bold.
1) 8,040
8,040
Location of the last significant place value is 3 and bar is over last significant digit that is 4. Number is not decimal so ending zero is ignored. Every non zero digit is a significant.
2) 0.0300
0.0300
Location is 3 and bar is over 0. Number has a decimal point so ending zero is not ignored but starting zeroes are ignored.
3) 699.5
699.5
Location is 4 and bar is over 5.
4) 2.000 x 10²
2.000 x 10²
Location is 4 and bar is over 0. This is because the number is decimal so trailing zeroes cannot be ignored. Also if we convert this number it becomes:
200.0 so last significant digit is 0 and location of last significant digit is 4.
5) 0.90100
0.90100
Location is 5 and bar is over 0. This is because in a number with decimal point starting zeroes are ignored but trailing zeroes after decimal point are not ignored. So we count from 9 and last significant digit is 0.
6) 90, 100
90, 100
Location is 3 and bar is over 1. This is because it is not a number with decimal point. So the trailing zeroes are ignored. The count starts from 9 and last significant is 1.
7) 4.7 x 10⁻⁸
4.7 x 10⁻⁸
Location is 2 and bar is over 7. This is because the starting zeroes in a number with a decimal point are ignored. So the first digit considered is 4 and last significant digit is 7. If we expand this number:
4.7 x 10⁻⁸ = 0.000000047 = 0.000000047
Here the starting zeroes are ignored because there is a decimal point in the number.
8) 10,800,000.0
10,800,000.0
Location is 9 and bar is over 0. Number has a decimal point so ending zero is not ignored and last significant figure is 0.
However if the number is like:
10,800,000. Then location would be 8 and bar is over 0.
9) 3.01 x 10²¹
3.01 x 10²¹
Location is 3 and bar is over 1. Lets expand this number first
3.01 x 10²¹ = 3.01 x 1000000000000000000000
= 3010000000000000000000
So this is the number:
3010000000000000000000
Since this is number does not have a decimal point so the trailing zeroes are ignored. Hence the count starts from 3 and the last significant figure is 1
10) 0.000410
0.000410
Location is 3 and bar is over 0. This is because the number has a decimal point so the ending zero is not ignored but the starting zeroes are ignored according to the rules given above. Hence the first significant figure is 4 and last significant figure is 0.