Measuring and Units

International System of Units Metric system SI Universally accepted and understood by scientist around the world

Derived units are a combination of base units Example: m/s

Density Density is a ratio that compares the mass of an object to its volume. Density = mass/volume D=m/v Units are g/L g/mL g/cm3

Temperature ◦C increase 1 unit at a time Kelvin increase 1 unit at a time Therefore to convert from ◦C to K K = 273 + ◦C

Degrees Celsius SI Unit is Kelvin Boiling point = 100 ◦C Freezing point = 0 ◦C SI Unit is Kelvin Boiling point = 373 K Freezing point = 273 K

Scientific Notation Contains a number and then raised to a power The exponent tell you how many times the factor must be multiplied by ten If the number is less then 1 the exponent is negative If the number is greater then 1 the exponent is positive

When adding or subtracting using exponents, the exponents must be the same If they are not the same in the problem you can change them so they are the same

When multiplying and dividing exponents the exponents do not have to be the same.

When multiplying first multiply the factors then you add the exponents When dividing first divide the factors then you subtract the exponents

Dimensional Analysis Dimensional analysis is a method focused on units that describe matter Use conversion factors to convert from one unit to another 35 m = 35000 mm Conversion factor 1m = 1000mm

Accuracy and Precision Accuracy refers to how close a measured value is to an accepted value Precision refers to how close a series of measurements are to each other

Percent Error Percent error is the ratio of error to an accepted value.

Percent Error A student performs an experiment and determines the density of an object to be 1.54 g/mL. The actual density is 1.58 g/mL. Find the students percent error.

Significant Figures Significant Figures (sig figs) are the digits that carry meaning contributing to its precision.

Rules for Sig Figs 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. 2) ALL zeroes between non-zero numbers are ALWAYS significant. 3) ALL final zeroes which are to the right of the decimal point are significant 4) Zeros that act as placeholders are not significant When in scientific notation if you can remove the zeros they are not significant

Examples Rule 1 – Rule 2 – 456 has 3 significant figures

Rule 3 – Rule 4 – 9.70 has 3 significant figures 0.0787 has only 3 significant figures 4350 has only 3 significant figures

Rounding A calculated number should only have the number of significant figures as the data with the fewest sig figs.

Rules for Rounding If the digit to the immediate right of the last significant figures is less than five, do not change the last significant figure We need only 3 sig figs 3.562  3.56

2. If the digit to the immediate right of the last significant figure is greater than five, round up the last significant figure 3 sig figs 1. 4.567  4.57

If the digit to the immediate right of the last significant figure is equal to five and is followed by a nonzero digit, round up the last significant figure 2.5351  2.54

If the digit to the immediate right of the last significant figure is equal to five and is not followed by a nonzero digit, look at the last significant figure. If it is an odd digit, round it up. If it is an even digit, do not round up. 2.5350  2.54 2.5250  2.52

Adding and Subtracting When you add or subtract measurements, your answer must have the same number of digits to the right of the decimal point as the value with the fewest digits to the right of the decimal point. Example: 1.24 mL + 12.4 mL = 13.84 mL – 13.8 mL

Multiplying and Dividing When multiplying and dividing, your answer must have the same number of sig figs as the measurement with the fewest sig figs. 3.65 cm x 3.20 x 2.05 cm = 23.944 cm3 = 23.9 cm3