number part 6 significant figures
What is the point of significant figures?
When carrying out a mathematical calculation your answer can't be more accurate than the values you used to calculate it. Significant figures are the digits of a number which are relevant in indicating how precise a number is.
When carrying out a mathematical calculation your answer can't be more accurate than the values you used to calculate it. Significant figures are the digits of a number which are relevant in indicating how precise a number is.
Lets look at an example.
Billy measures his teachers' desk as accurately as he can with a tape measure and finds it is 2.09 m long and 1.59 m wide. He then works out its area.
Area = length x width
= 2.09 x 1.59
= 3.3231 m squared
Billy measures his teachers' desk as accurately as he can with a tape measure and finds it is 2.09 m long and 1.59 m wide. He then works out its area.
Area = length x width
= 2.09 x 1.59
= 3.3231 m squared
Notice that the answer has more precision than the values used to calculate it. There are 5 significant figures in the product (answer) but only 3 significant figures in the starting figures of 2.09 and 1.59 (the multiplicand).
Our answer needs to be rounded to 3 significant figures, which is 3.32 m squared. We will come back to this later.
Our answer needs to be rounded to 3 significant figures, which is 3.32 m squared. We will come back to this later.
rules of significant figures
(1) Non zero digits (1,2,3,4,5,6,7,8 and 9) are always significant
(2) Any zeros between two significant digits are significant.
(3) A final zero or trailing zeros in the decimal portion ONLY are significant.
(2) Any zeros between two significant digits are significant.
(3) A final zero or trailing zeros in the decimal portion ONLY are significant.
identifying Significant figures
State the number of significant figures according to the rules above.
1) 0.0800 - the 800 part of the number is significant (it has 3 significant figures)
2) 0.022 - the 22 part of the number is significant (it has 2 significant figures)
3) 470 - the 47 part of the number is significant (it has 2 significant figures)
4) 470. - all 3 digits thanks to the decimal point. (it has 3 significant figures)
4) 30.0 - all digits are significant (it has 3 significant figures)
5) 809.005 - all the numbers are significant (it has 6 significant figures)
6) 16000 - only the 16 part of the number is significant ( It has 2 significant figures)
1) 0.0800 - the 800 part of the number is significant (it has 3 significant figures)
2) 0.022 - the 22 part of the number is significant (it has 2 significant figures)
3) 470 - the 47 part of the number is significant (it has 2 significant figures)
4) 470. - all 3 digits thanks to the decimal point. (it has 3 significant figures)
4) 30.0 - all digits are significant (it has 3 significant figures)
5) 809.005 - all the numbers are significant (it has 6 significant figures)
6) 16000 - only the 16 part of the number is significant ( It has 2 significant figures)