Day 02­ Measurement, Sig Figs, Rounding By the end of today you should be able to:
1. Distinguish between exact and measured numbers
2. Identify the number of significant digits in a measurement
3. Round to a specified number of significant digits
1. Exact Numbers
All counted quantities are exact and contain an infinite number of significant digits. Only whole numbers are possible.
ex. Count the students in the class
Numbers obtained from definitions are exact and have an infinite number of significant digits.
ex. 1 km has exactly 1000 m
2. Measurements and Significant Digits
Measurements are not exact. They are comparisons to a standard. In the process of measuring there is some degree of error or uncertainty, which depends on the equipment you use.
Scientists want to record the most accurate number for any measurements they make. To measure to the correct number of significant digits, record all certain digits, plus one uncertain digit. Day 02­ Measurement, Sig Figs, Rounding Rules for Significant Digits 1 All non­zero digits are significant.
ex. 123.45 has 5 sig figs
ex. 5.71 has 3 sig figs
2 All zeroes between non­zero digits are significant.
ex. 404 has 3 sig figs
ex. 502.0001 has 7 sig figs
3 Trailing zeroes to the RIGHT of the decimal are significant.
ex. 2.0 has 2 sig figs
ex. 3.400 has 4 sig figs
4 All digits used in scientific notation are significant. ex. 1.5 x 10 3 has 2 sig figs
ex. 1.50 x 10 3 has 3 sig figs
Note: A number with no decimal and trailing zeros like 1500 may have 2,3 or 4 significant digits. Avoid confusion by using scientific notation.
ex. 20 may have 1 or 2 sig figs
5 Leading zeroes are NOT significant, they are place holders.
ex. 0.003 has 1 sig fig
ex. 0.22 has 2 sig figs
Day 02­ Measurement, Sig Figs, Rounding What measurements would your record in your lab book for the following? How many sig figs does each have?
(d) Thermometer calibrated in oC
(e) Pressure gauge calibrated in psi
(f) Balance calibrated in grams
Identify the number of significant digits.
1) 3782 m 3) 0.004 L 5) 1.010 cm 7) 1000 people
2) 2000 g 4) 0.9740 km 6) 0.09097 ºC
8) 42 980 cats Pairs Check Activity: Significant Digits
Partner A does #1
Partner B does #2
Partner A does #3 ...etc.
Check your partner's work after each set of questions
3. Rounding
Read through 'Guidelines for Rounding Off Using Significant Digits' on the back of BLM G­24
Day 02­ Measurement, Sig Figs, Rounding Significant Digits and Rounding
Round to 1 sd
Round to 2 sd
Round to 3 sd
The even odd rule
If it ends in 5 or 50 or 500 or 5000 etc
Look at the digit before the 5
Round to 3 s.d
If it is EVEN round down 3.65
3.650
If it is ODD round up 3.75
3.750
Round to 3 s.d
a) 3.752
c) 0.04542
e) 76.23
Day 02­ Measurement, Sig Figs, Rounding Calculations
When adding or subtracting measured quantities the answer must have the same number of decimal places as the quantity with the smallest number of significant digits.
ex.
When multiplying, dividing, finding roots or squares of measured quantities, the answer must have the same number of significant digits as the quantity with the smallest number of significant digits used in the calculation.
ex.
Day 02­ Measurement, Sig Figs, Rounding