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Significant Figures Notes and Practice, Exams of Mathematics

University of Dayton (UD)Mathematics

Instructions and examples for determining the number of significant figures in measurements, rounding rules, and applying significant figure rules in calculations such as addition, subtraction, multiplication, and division.

What you will learn

How many significant figures are there in the measurement 213 mg?
How many significant figures are there in the measurement 81000 pg?
What is the number of significant figures in the measurement 3001 dm?

Typology: Exams

2021/2022

Uploaded on 09/27/2022

teap1x 🇺🇸

4.7

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231 documents

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Sig Fig Notes & Practice Name: _____________________________________________________ Date: ________

2. Measure the length, in centimeters, of each item in the images below.

Uncertainty in Measurement: When reading an instrument…Write all the digits you see + 1 more that you estimate

1. Measure the volume, in mL, of each liquid in the images below.

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Download Significant Figures Notes and Practice and more Exams Mathematics in PDF only on Docsity!

Sig Fig Notes & Practice Name: _____________________________________________ Date:

2. Measure the length, in centimeters, of each item in the images below. Uncertainty in Measurement: When reading an instrument…Write all the digits you see + 1 more that you estimate 1. Measure the volume, in mL, of each liquid in the images below.

Sig Fig Rules

Count all non-zero digits (ex. 1234 = 4 sig figs 139 = 3 sig figs)
Counting Zeros a) Count zeros that are “sandwiched” between non-zero digits (ex. 708 = 3 sig figs 1008 = 4 sig figs) b) Count zeros at the end of a number only if there is a decimal point (ex. 100 = 1 sig fig 100. = 3 sig figs) c) NEVER count zeros at the beginning of a number (i.e. start counting sig figs with the first non-zero digit) (ex. 0.000 51 = 2 sig figs)
Count all the digits in scientific notation (ex. 3. 42 x 10^5 = 3 sig figs 1. 000 x 10-^8 = 4 sig figs)
Exact numbers. Numbers that are counted rather than measured are called exact numbers. For example, you count 3 apples or perform 5 trials. Since there is no uncertainty in these numbers, exact numbers have an infinite number of siginificant figures and are not used to determine the number of significant figures when doing calculations.

3. Determine the number of sig figs in each value. a) 213 mg b) 3001 dm c) 81000 pg d) 6.00 L e) 0.0021 km f) 0.420 g g) 92.00 cm h) 7. 80 x 103 m

Rules for Rounding

Determine the number of significant digits to keep.
Moving left to right, start counting significant digits with the first non-zero digit.
Stop once you reach the last significant digit to keep. Look at the digit directly to the right of the last significant digit. a) If the digit to the right is less than 5, then the preceding digit stays the same. Example: 1.3 46 m rounds to 1.3 m (note that only the first number to the right of the last significant digit is used to round, i.e. the 6 does not round the 4 to a 5 and then the 3 to a 4). b) If the digit to the right is equal to or greater than 5, then the preceding digit is increased by one. Example: 1.37 m rounds to 1.4 m
When the last significant digit is in the tens, hundreds, thousands place or any other multiple of ten, round according to Rules #1-3 above, but also write a zero, “ 0 ”, for each eliminated digit between the last significant digit and the decimal point. Do not write a decimal point. Example: 34914.849 m rounded to two significant figures is 35000 m In most cases it will be easier to first convert to scientific notation and then round for sig figs. Example: 34914.849 m = 3.4914849 x 10^4 m which rounded to two significant figures is 3.5 x 10^4 m which is the same value as 35000 m

7. Calculate and round answer to the correct number of sig figs. a) (320. − 22.7) x 3.8 b) (1.80 x 3.4) + 32.00 c) (1.80 x 25.3) + 32 d) ( 6. 8 + 4. 701 ) ( 21. 25 − 18 ) e) ( 3. 65 )( 2. 10 ) ( 2. 1134 )( 42. 1 ) f) ( 14. 86 + 13. 7 )( 65. 346 − 4. 10 ) ( 43. 888 − 32. 888 ) g) Average the following masses: 0.621 g, 1.614 g, 0.08456 g, 0.4 g h) Calculate the density of an object with a mass of 760 g and volume of 15.0 mL i) Calculate the quantity of heat transferred when a 0.050 g object with a specific heat of 2.06 J/g°C is heated from an initial temperature of 85°C to a final temperature of 90.°C. j) Calculate the percent error of a density experiment in which the experimental density value is determined to be 5.01 g/mL and the accepted value in a handbook is reported as 5.850 g/mL.