1:3SCH 3U-ACCURACY, PRECISION and SIGNIFICANT FIGURES
- PRECISION IN MEASUREMENT
Scientists always try to make their measurements as precise* as they can.
* Do not confuse the term accuracy with the term precision.
Accuracy refers to whether you are actually measuring what you intend. For example you may find the mass of a flask to be 164.178 g – very precise. But if the flask was wet or dirty then this measurement is inaccurate.
They also need a way of communicating exactly how precise a particular measurement is.
5.2 g and 5.20 g represent measurements of the same size but a different precision.
5.2 g means the measurement is closer to 5.2 g than to 5.1 g or to 5.3 gthe precision is ±0.1
5.20 g means the measurement iscloser to 5.20 g than to 5.19 g or to 5.21 gthe precision is ±0.01
- SIGNIFICANT FIGURES
The precision of a measurement is expressed in terms of significant figures (sf).
The value 5.2 has 2 sf while 5.20 has 3 sf. The extra zero at the end makes this measurement more precise and is included as a sf. A zero before the first digit does not count as significant, as precision is not increased,
0.50 m is the same as 50 cm (both have 2 sf) * Rule: trailing “zeros” count - leading “zeros” don’t count
Practice:State the number of sf in each of the following
0.0420 km (……….) 4.1 g (……….)3.9120 m (……….)0.031 W (……….)
0.310 W (……….)0.00310 W (……….)0.037 km (……….) 3.037 km (……….)
- EXPONENTIAL (SCIENTIFIC) NOTATION
Scientific notation is used to control the number of significant digits in both large & small numbers.
The rule here is simple – ignore the exponent! 3.4x103 has 2 sf; so does 3.4x10-5 & 3.4 x 108.
EX: 2000 km could have 1 sf, or 2, or 3, or 4; but 2 x 103 km is unambiguously expressed to 1 sf while 2.00 x 103 km is more precisely expressed with 3 sf.
Practice: State the number of sf in each of the following
4.52 x 104 (……..…) 5.915 x 10–7(……..…)2 x 10–3 (…..……)3.001 x 10–5 (…..……)
Convert the following measurements from SN
4 x 104 = ………..…….. 4.0 x 10–4= ………….…….. 3.2 x103 = ………....…….. 3.200x103 = ……….……..
- WORKING WITH SIGNIFICANT FIGURES
There are 2 rules you should remember
a)The result of a calculation cannot be expressed to a greater number of sf than the least precise of the measurements or estimates.
b)The working in a calculation should be expressed to at least 1 more sf than the result will be. Don’t round off until the end.
Ex 1: A car travels 625.4 km in 8.2 h. Calculate its velocity.
Velocity = distance / time
= 625.4/8.2 km/h * 8.2 h is the least precise measurement – 2 sf
= 76.3 km/h
= 76 km/h ** the answer can have no more than 2 sf of precision
Ex 2: A teacher gives 66.0 g of candy to each of her 28 students. How much candy does she give out?
Total mass = 28 x 66.0 g
= 1848 g The number 28 is counted so does not limit the precision
= 1.85kg ( 3 sf )of the answer – so answer can be expressed to 3 sf
Note: Units can also be used to control sf
Ex 3: A 694 kg concrete slab is 1.47 m long, 1.2 m wide & 0.500 m high. Calculate its density.
Volume of slab = length x width x height
=1.47 m x 1.2 m x 0.500 m
= 0.882 m3* this is not your answer so don’t round yet
Density = mass / volume = 694 kg / 0.882 m3
= 746.8 kg/m3 * the least precise measurement is 1.2 m – 2 sf
= 7.5x 102 kg/m3so the final answer should only have 2 sf
Practice:
Read : Measurement & uncertainty, Significant digits, Accuracy & precision (pg-15-22)
Practice: 1 & 2 pg 18;
3 pg 22
1-6 pg 24