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1.3 Measurements

Learning Objective

  1. Express quantities properly, using a number and a unit.

A coffee maker’s instructions tell you to fill the coffeepot with 4 cups of water and use 3 scoops of coffee. When you follow these instructions, you are measuring. When you visit a doctor’s office, a nurse checks your temperature, height, weight, and perhaps blood pressure (Figure 1.6 "Measuring Blood Pressure"). The nurse is also measuring.

Figure 1.6 Measuring Blood Pressure

A nurse or a doctor measuring a patient’s blood pressure is taking a measurement.

Chemists measure the properties of matter and express these measurements as quantities. A quantityAn amount of something. is an amount of something and consists of a numberHow many (or how much) of something in a quantity. and a unitThe scale of measurement for a quantity.. The number tells us how many (or how much), and the unit tells us what the scale of measurement is. For example, when a distance is reported as “5 kilometers,” we know that the quantity has been expressed in units of kilometers and that the number of kilometers is 5. If you ask a friend how far he or she walks from home to school, and the friend answers “12” without specifying a unit, you do not know whether your friend walks—for example, 12 miles, 12 kilometers, 12 furlongs, or 12 yards. Both a number and a unit must be included to express a quantity properly.

To understand chemistry, we need a clear understanding of the units chemists work with and the rules they follow for expressing numbers. The next two sections examine the rules for expressing numbers.

Example 3

Identify the number and the unit in each quantity.

  1. one dozen eggs
  2. 2.54 centimeters
  3. a box of pencils
  4. 88 meters per second

Solution

  1. The number is one, and the unit is dozen eggs.
  2. The number is 2.54, and the unit is centimeter.
  3. The number 1 is implied because the quantity is only a box. The unit is box of pencils.
  4. The number is 88, and the unit is meters per second. Note that in this case the unit is actually a combination of two units: meters and seconds.

Skill-Building Exercise

    Identify the number and the unit in each quantity.

  1. 99 bottles of soda

  2. 60 miles per hour

  3. 32 fluid ounces

  4. 98.6 degrees Fahrenheit

Concept Review Exercise

  1. What are the two necessary parts of a quantity?

Answer

  1. The two necessary parts are the number and the unit.

To Your Health: Dosages

As we saw in the chapter-opening essay, a medicine can be more harmful than helpful if it is not taken in the proper dosage. A dosage (or dose) is the specific amount of a medicine that is known to be therapeutic for an ailment in a patient of a certain size. Dosages of the active ingredient in medications are usually described by units of mass, typically grams or milligrams, and generally are equated with a number of capsules or teaspoonfuls to be swallowed or injected. (For more information about mass, see Section 1.6 "The International System of Units".) The amount of the active ingredient in a medicine is carefully controlled so that the proper number of pills or spoonfuls contains the proper dose.

Most drugs must be taken in just the right amount. If too little is taken, the desired effects will not occur (or will not occur fast enough for comfort); if too much is taken, there may be potential side effects that are worse than the original ailment. Some drugs are available in multiple dosages. For example, tablets of the medication levothyroxine sodium, a synthetic thyroid hormone for those suffering from decreased thyroid gland function, are available in 11 different doses, ranging from 25 micrograms (µg) to 300 µg. It is a doctor’s responsibility to prescribe the correct dosage for a patient, and it is a pharmacist’s responsibility to provide the patient with the correct medicine at the dosage prescribed. Thus, proper quantities—which are expressed using numbers and their associated units—are crucial for keeping us healthy.

Key Takeaway

  • Identify a quantity properly with a number and a unit.

Exercises

  1. Why are both parts of a quantity important when describing it?

  2. Why are measurements an important part of any branch of science, such as chemistry?

  3. You ask a classmate how much homework your chemistry professor assigned. Your classmate answers, “twenty.” Is that a proper answer? Why or why not?

  4. Identify the number and the unit in each quantity.

    1. five grandchildren
    2. 16 candles
    3. four score and seven years
    4. 40 days and 40 nights
    5. 12.01 grams
    6. 9.8 meters per second squared
    7. 55 miles per hour
    8. 98.6 degrees Fahrenheit

Answers

  1. The number states how much, and the unit states of what. Without the number and the unit, a quantity cannot be properly communicated.

  2. No, it is not a proper answer; you do not know whether the professor meant homework problem number 20 or 20 homework problems.