Units and Scientific Notation

Common Units The units we use represent different kinds of scientific measurements. Common measurements (unit types) are: time, distance, volume, temperature, mass, energy, pressure, and # of particles

Common Units The table below organizes SI base units for each type of measurement. Unit Type Base Unit mass kilogram (kg) time second (s) volume liter (L) temperature kelvin (K) distance meter (m) pressure atmosphere (atm) # particles mole (mol) energy joule (J)

Scientific Notation In chemistry you will be using data that are measured in very small and very large scales. Scientific Notation allows us to express these very large or small numbers in simpler ways. We express numbers with a single units digit, additional digits behind the decimal, then multiply by 10 raised to a power to show the scale of the measurement.

Scientific Notation 1748590 would be expressed as: 1.748590 × 106 6.743 × 10-4 For decimal shifting and exponent changes remember the acronym: LIRD shifting the decimal left, increases the exponent shifting the decimal right, decreases the exponent

Comprehension Check 1. Express 452,000,000,000 using scientific notation. 2. Express 3.574 ×10–4 using standard notation. 3. Express 3.2 ×1012 using standard notation. 1) 4.52 × 1011 2) 0.0003574 3) 3,200,000,000,000 4) 8.4×10-7 4. Express 0.00000084 using scientific notation.

Modifying Scale with Prefixes We’ve seen how using scientific notation can help us to write numbers more easily. Adding a prefix to the base unit can be a simple way to change the scale and we can avoid the need to use scientific notation.

Comprehension Check 5. Convert 0.550 seconds (s) into milliseconds (ms). 6. Convert 6.54 kilometers (km) into meters (m). 7. Convert 32 decigrams (dg) to micrograms (μg). 5) 550 ms 6) 6540 m 7) 3.2×106 μg 8) 9.34×10-4 ML 8. Convert 934,000 milliliters (mL) into megaliters (ML).

Uncertainty of Measurements The number of digits shown in a measurement is limited by the scale on the measuring device. The graduated cylinder is precise to the ones digit. We record a measurement to the tenths (0.1) digit. (one estimated digit)

Uncertainty of Measurements The volume measurement would be 43.0 mL. Each digit communicates scale and is significant. 40 mL would be too vague. (tools are more specific) 43.00184 mL would be too specific. (tools are not this precise)

Uncertainty in Calculations Let’s say we want to determine the density of that liquid sample. The mass is measured at 44.54 g. The volume is measured at 43.0 mL Density is g/mL so we must divide the two numbers.

Uncertainty in Calculations The mass is measured at 44.54 g. 44.54 g ÷ 43.0 mL = 1.03581… g/mL The volume is measured at 43.0 mL Our answer is limited to have the same number as the LEAST precise measurement. NOTE: For addition and Subtraction, we round to the leftmost uncertain digit. We will do this in lab. Our final answer must be rounded to only 3 digits. 1.04 g/mL

Recognizing Significant Digits 595 1) All non-zero digits are always significant. Even though 500 has only 1 measured digit, the zeros must be written to communicate the scale of the measurement in that unit. 2) Zeroes between non-zero digits are always significant. 505 500 Even though 500 has only 1 measured digit, the zeros must be written to communicate the scale of the measurement in that unit. 3) For numbers  1, zeroes at the end are never significant unless followed by a decimal point. 500.

Recognizing Significant Digits 4) For numbers  1, zeroes before a non-zero are never significant. 0.00505 5) All digits following a non-zero in a number with a decimal are always significant. 505.00

Comprehension Check 9. How many significant digits are in the measurement 54.59? 10. How many significant digits are in the measurement 0.535? Identify the type of zeros we see here. 9) 4 10) 3, leading 11) 2, trailing w/out a decimal 11. How many significant digits are in the measurement 3900? Identify the type of zeros we see here.

Comprehension Check 12. How many significant digits are in the measurement 32.00? Identify the type of zeros we see here. 13. How many significant digits are in the measurement 0.084? Identify the type of zeros we see here. 12) 4, trailing w/ decimal 13) 2, leading 14) 3, captive 14. How many significant digits are in the measurement 105? Identify the type of zeros we see here.

Comprehension Check 15. How many significant digits are in product of 354 and 0.095? Solve this problem and round your answer. 16. How many significant digits are in quotient of 40.00 352 ? Solve this problem and round your answer. 15) 2, calculates to 33.63, but rounds to 34 16) 3, calculates to 0.11363…, but rounds to 0.114