Types of measurement

 



Two types of measurement

  • Qualitative: Give results in a descriptive, nonnumeric manner.
  •  Ex) If you test with your hand to see if someone has a fever you performed a qualitative measurement.
  • These are subject to personal biases though, because it all depends on your perception.
  • Color is an example of qualitative measurements.

Quantitative

  • Quantitative: Give results in a definite form, usually as numbers or units.
  • For example the thermometer might reveal that a persons temperature is 39.2oC (102.5oF).
  • This measurement has a definite value that can be compared with the person’s temperature at a later time to check for changes.
  • This measurement, no matter how definite, can be no more reliable than the instrument used to make the measurement and the care with which it is used and read.

Why we use scientific notation

  • Scientific Notation: In chemistry very large and small numbers are used frequently.
  • For instance the mass of an atom of gold is 0.000 000 000 000 000 000 000 327 grams.
  • A gram of hydrogen contains 602,000,000,000,000,000,000,000 hydrogen atoms.
  • Writing and using such numbers becomes very cumbersome.
  • You can work with these numbers more easily with these numbers by writing them in scientific or exponential notation.

Scientific notation cont.

  • In Scientific notation a number is written as the product of two numbers: a coefficient and 10 raised to a power.
  • Ex) 2.3 x 104 is the same as 23,000. The coefficient in the number is 2.3.
  • In this notation the coefficient is always a number greater than or equal to one and less than ten.
  • The power of ten in this example is 4.
  • The exponent indicates how many times the coefficient 2.3 must be multiplied by 10 to equal the number 23,000.

Positive exponents

  • For numbers greater than ten the exponent is positive and equals the number of places you must move the original decimal place to the left.
  • I.e. 23,000 moves 4 places

Negative powers

  • For numbers less than one, the value of the exponent equals the number of places the original decimal place has been moved to the right.
  • Ex 0.0000081 = 8.1 x 10-6
  • which means that the coefficient needs to be divided by that power of 10
  • ex. 8.1 / (10 x 10 x 10 x 10 x 10 x 10) = 0.0000081.

Multiplication and Division

  • Sci. note makes calculating more straightforward.
  • To multiply numbers written in sci. note. Multiply the coefficients and add the exponents.
  • Ex) (6.0 x 10 3) x (2.0 x 10 3) =
  • (6.0 x 2.0) x 10 (3 + 3) =
  • 12.0 x 10 6

Division

  • Division: divide the coefficients then subtract the exponent in the denominator from the exponent in the numerator.
  • Ex) 20.0 x 10 5 / 4.0 x 10 3 =
  • (20.0 / 4.0) x 10 (5-3) =
  • 5 x 10 2

Addition and subtraction

Before you add or subtract numbers they must be in the same power of ten.
•You must make them the same because the exponent determines the decimal place.
•The decimal place must be aligned before you can add or subtract a number.
•Ex) 3.4 x 10 4 + 5.8 x 10 3
•you need to change one exponent to match, doesn’t really matter which.
•Let’s go with changing 5.8 x 10 3 to 0.58 x 10 4
If you want to make the exponent larger move the decimal to the left, smaller move it to the right
•Now just add the coefficients and include the power at the end 3.4 + 0.58 = 3.98 x 10 4