### Measuring up with metric prefixes

**Directions for teachers:** Students should discuss answers to the first set of questions before reading the *Science News* article “The metric system is growing. Here’s what you need to know” and answering the second set of questions. A version of the article, “The metric system has gained new prefixes,” appears in the January 14, 2023 issue of *Science News*.

To review the purpose of units in science and the importance of using standard units versus relative values, you can pull questions from the “Why use units” discussion lesson plan.

**Want to make it a virtual lesson?** Post the online *Science News *article to your virtual classroom. Discuss the article and questions with your class on your virtual platform.

**Prefixing the metric system**

1. Give at least four examples of words with prefixes and underline each prefix. Leave the root of the word without an underline. Compare the prefixes. What is similar about them and what is different?

*Student answers will vary. Examples may include unhappy, extraordinary, millimeter, kilogram, etc.*

2. What does each prefix in your examples tell you about the meaning of each word? Based on your examples, how would you define a prefix?*Student answers will vary. “Un-” means not, “extra-” means beyond, “milli-” means one thousandth and “kilo-” means one thousand. A prefix is attached to the front of a root word (happy, meter, gram, etc.) to create a derivative of the root word. The meaning of the new word is typically based on a combination of the prefix’s meaning with the root word’s meaning.*3. Give examples of root words used in the metric system, or the International System of Units (SI). What’s the purpose of these words? Give at least three examples, making sure to include their abbreviations and explain what the words mean.

*The metric system’s root words are units of measure for types of data. A meter (m) is a base unit of length, a gram (g) is a base unit of mass and a liter (L) is a base unit of volume.*

4. What are four common metric, or SI, prefixes. What do the prefixes mean on their own and how are they abbreviated?

*Milli- (m) means one thousandth, kilo- (k) means one thousand, deci- (d) means one tenth and centi- (c) means one hundredth.*

5. Based on your answers to the previous questions, define the terms “kilogram” and “milliliter.”

*A kilogram is a measure of mass equal to one thousand grams. A milliliter is a measure of volume equal to one thousandth of a liter.*

**Converting units**

1. The *Science News* article pairs the new metric prefixes ronna-, quetta-, ronto- and quecto- with grams, the base metric unit of mass. Is each prefixed unit (ronnagram, quettagram, rontogram and quectogram) larger or smaller than the base unit (gram)? Write a conversion factor, or unit factor, that converts each prefixed unit to the base unit.*Ronnagram and quettagram are both larger than a gram. One ronnagram is equal to 10 ^{27} grams, and one quettagram is equal to 10^{30} grams. Rontogram and quectogram are both smaller than a gram. One gram is equal to 10^{27} rontograms or 10^{30} quectograms. *

2. According to the online *Science News* article, Earth is six ronnagrams, Jupiter is two quettagrams, an electron is about one rontogram and one bit of data on a mobile phone is roughly one quectogram. Using the conversion factors you came up with, convert each mass to grams. Show how your units cancel using dimensional analysis, or the Factor Label Method.

*6 ronnagrams is 6 x 10 ^{27} grams. 2 quettagrams is equal to 2 x 10^{30} grams. 1 rontogram is equal to 1 x 10^{-27} grams. 1 quectogram is equal to 1 x 10^{-30} grams*.

3. Why are prefixes useful for expressing measurements? Think about your answers to the previous two questions.

*Prefixes are useful for scaling the base unit to easily express a measured quantity that may be very large or very small. For example, the mass of the Earth is a very large number of grams that’s hard to write out and conceptually understand. It’s much easier to write and understand 6 ronnagrams than it is to write and understand 6,000,000,000,000,000,000,000,000,000 grams, or even **6 x 10 ^{27} grams.*