i have to round each to 3 significant figures, then to one significant figure, in standard form, how?
a) 87.073 m
b) 4.3621 x 10^8 m
c) 0.01552 m
d) 9009 m
e) 1.7777 x 10^-3 m
f)629.55 m
okay, so e) would be 2.77->2 but how would the others be to 1 significant number if there over?
(e) 1.7777 -> 1.78 -> 2
I have no idea what if there over? means.
In each case, round to 3 digits, then round that result to 1.
Yes
To round each value to 3 significant figures in standard form, you need to follow these steps:
Step 1: Identify the first non-zero digit from the left (most significant digit).
Step 2: Count the number of digits from the first non-zero digit (including zeros) until you reach 3 significant figures.
Step 3: If the digit to the right of the 3 significant figures is 5 or greater, round up the last significant figure. If it is less than 5, leave the last significant figure unchanged.
Now, let's apply these steps to each value:
a) 87.073 m:
Step 1: The first non-zero digit is 8.
Step 2: There are 5 digits from the first non-zero digit.
Step 3: The digit to the right of the 3rd significant figure is 3, so the last significant figure remains unchanged.
Result: 87.1 m
b) 4.3621 x 10^8 m:
Step 1: The first non-zero digit is 4.
Step 2: There are 5 digits from the first non-zero digit.
Step 3: The digit to the right of the 3rd significant figure is 2, so the last significant figure remains unchanged.
Result: 4.36 x 10^8 m
c) 0.01552 m:
Step 1: The first non-zero digit is 1.
Step 2: There are 3 digits from the first non-zero digit.
Step 3: The digit to the right of the 3rd significant figure is 5, so the last significant figure is rounded up.
Result: 0.0156 m
d) 9009 m:
Step 1: The first non-zero digit is 9.
Step 2: There are 4 digits from the first non-zero digit.
Step 3: There is no significant figure to the right of the 3rd significant figure.
Result: 9000 m
e) 1.7777 x 10^-3 m:
Step 1: The first non-zero digit is 1.
Step 2: There are 4 digits from the first non-zero digit.
Step 3: The digit to the right of the 3rd significant figure is 7, so the last significant figure is rounded up.
Result: 1.78 x 10^-3 m
f) 629.55 m:
Step 1: The first non-zero digit is 6.
Step 2: There are 5 digits from the first non-zero digit.
Step 3: The digit to the right of the 3rd significant figure is 5, so the last significant figure remains unchanged.
Result: 629 m
To round each value to one significant figure in standard form, you follow similar steps:
Step 1: Round the value to one significant figure.
Step 2: Determine the exponent if it is in standard form (scientific notation).
Now, let's apply these steps to each value:
a) 87.073 m:
Step 1: Round to one significant figure: 90.
Result: 9 x 10^1 m
b) 4.3621 x 10^8 m:
Step 1: Round to one significant figure: 4 x 10^8.
Result: 4 x 10^8 m
c) 0.01552 m:
Step 1: Round to one significant figure: 0.02.
Result: 2 x 10^-2 m
d) 9009 m:
Step 1: Round to one significant figure: 9000.
Result: 9 x 10^3 m
e) 1.7777 x 10^-3 m:
Step 1: Round to one significant figure: 2 x 10^-3.
Result: 2 x 10^-3 m
f) 629.55 m:
Step 1: Round to one significant figure: 600.
Result: 6 x 10^2 m
By following these steps, you can effectively round each value to the desired number of significant figures and express them in standard form when necessary.
(a) 87.073 -> 87.1 -> 90
(b) 4.3621 -> 4.36 -> 4
and so on
what do you get?