1.3: Measurements

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Skills to Develop

To 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 \(\PageIndex{1}\)); the nurse is also measuring.

Figure \(\PageIndex{1}\): Measuring Blood Pressure. A nurse or a doctor measuring a patient’s blood pressure is taking a measurement. Figure used with permission from Wikipedia.

Chemists measure the properties of matter using a variety of devices or measuring tools, many of which are similar to those used in everyday life. Rulers are used to measure length, balances (scales) are used to measure mass (weight), and graduated cylinders or pipettes are used to measure volume. Measurements made using these devices are expressed as quantities. A quantity is an amount of something and consists of a number and a unit. 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 \(\PageIndex{1}\)

Identify the number and the unit in each quantity.

one dozen eggs
2.54 centimeters
a box of pencils
88 meters per second

Answer a: The number is one, and the unit is dozen eggs.
Answer b: The number is 2.54, and the unit is centimeter.
Answer c: The number 1 is implied because the quantity is only a box. The unit is box of pencils.
Answer d: 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.

Exercise \(\PageIndex{1}\)

Identify the number and the unit in each quantity.

99 bottles of soda
60 miles per hour
32 fluid ounces
98.6 degrees Fahrenheit

Concept Review Exercise

What are the two necessary parts of a quantity?

Answer

The two necessary parts are the number and the unit.

Key Takeaway

Identify a quantity properly with a number and a unit.

Exercises

Why are both parts of a quantity important when describing it?
Why are measurements an important part of any branch of science, such as chemistry?
You ask a classmate how much homework your chemistry professor assigned. Your classmate answers, “twenty.” Is that a proper answer? Why or why not?
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

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

2. Measurements are needed to carry out experiments.

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

The number is 5, and the unit is grandchildren.
The number is 16, and the unit is candles.
The number is 4 score and 7 (= 87), and the unit is years.
The number is 40, and the units are days and nights.
The number is 12.01, and the unit is grams.
The number is 9.8, and the unit is meters per second squared.
The number is 55, and the unit is miles per hour.
The number is 98.6, and the unit is degrees Fahrenheit.