# Sizing Up

For most people, the actual sizes of microscopic cells and other very small objects can come as a big surprise. In this activity, cells, organelles, bacteria, and viruses are “sized up” one million times.

- This Sizing Up Objects list
- This Sizing Up Data table
- This Metric Measurements chart
- At least two index cards for each participant, or each pair working together
- Meter sticks or metric measuring tapes (enough for group use)
- Metric rulers
- Large sheet of paper
- Marker
- Optional: String, scissors

*Note: This activity works best when done in a group or classroom setting.*

- Select some or all of the objects from the
*Sizing Up Objects*list that will be most useful for your group or class. (You can also add objects of your own.) - For each object chosen, write the name of the object and its actual dimensions on an index card (one object per card). Do not include the “Sized Up by 10
^{6}” information on the card. - Distribute the cards so that each participant, or pair of participants, has at least two index cards with objects of different sizes on them.
- Using the information from the
*Sizing Up Data*table, prepare your own table on a large piece of paper. Your table should list all the objects being used by the group, including the actual sizes of each object, but leaving the “Sized Up” and “Sized-Up Model” columns blank.

Working alone or in pairs, have participants “size up” the objects on their cards by multiplying each object’s actual size by one million, or 10^{6}. Then, have people use measuring tools to find something to model the sized-up versions of their objects. Encourage participants to be creative when choosing something to model their sized-up objects. Some of the models may be larger than the room! If the models are too large to easily measure with a meter stick or other measuring tools, use string and scissors. Cut a piece of string that is the same length as the model, then measure the length of the string.

How do these sized-up models compare to each other? Fill in your table as participants share their results and their models. Are the results surprising? How do the sizes of small things compare to each other? How do these objects compare to each other? Which is the smallest? Which is the largest? How many of the smaller objects could fit inside the larger objects?

If you’re working with younger participants, you may want to supply the “Sized Up by 10^{6}” sizes of the cells and structures, and have them find models that are similarly sized.

Understanding the relative sizes of cells, bacteria, and viruses is a helpful way to understand the nature of disease.

It may seem reasonable to think that viruses are relatively large because of the severity of the diseases they cause. In fact, viruses—including the one that causes COVID-19—are so tiny that special care needs to be taken to avoid infection.

When compared to cells and bacteria, viruses—which consist only of proteins and nucleic acids—are the smallest. Bacteria, the next largest group, contain several types of organelles, but have no nucleus. Plant and animal cells contain many types of organelles, and their DNA is condensed into chromosomes that are within the cell’s nucleus. Plant cells tend to be larger than animal cells because of their very large central vacuole used in water regulation.

The human egg cell, by comparison, is very large, because it must contain all the cytoplasm, organelles, proteins, and other cellular components required for early embryonic development. The human sperm is designed to be highly mobile. It carries only what it needs to reach the egg and fertilize it: DNA, mitochondria, a centrosome, a few enzymes, and a tail-like flagellum.

DNA is extremely thin, but very long. To package DNA within the confines of a cell’s nucleus, it is tightly interwoven with proteins and coiled into chromosomes.

Use inexpensive and available materials (paper, packaging foam, tape, and so on) to make models of selected cells. Search the Exploratorium’s Microscope Imaging Station, or other Internet sites, for pictures of cells, viruses, and bacteria.

The sizes for cells, organelles, and other objects used in this activity are approximations and sometimes averages. Each of these objects exists in a range of dimensions. Cells of a particular type are not always identical in size, nor are their organelles. The sizes do not typically vary by orders of magnitude. You may find other sizes listed in other publications. Some of these differences may be due to the types of cells being studied, the method used to calculate “typical” size, or the type of sample preparation used.

Multiplying exponents may be unfamiliar to some. Using exponents provides a shorthand way of expressing very large and very small numbers. Negative exponents don’t represent negative numbers, but fractions. Do you see a pattern in the chart below? What do you notice about the number 1? When learning to multiply exponents, try writing out the numbers in expanded form, putting positive exponents in the numerator of the fraction and negative exponents in the denominator of the fraction. You’ll see you have some number of 10s in the numerator and some number of 10s in the denominator. Since 10/10 = 1, you can think of each 10 pair (one in the numerator and one in the denominator) as a 1.

$$ $$

Number | Expanded | Exponent |
---|---|---|

1,000,000 | 10 x 10 x 10 x 10 x 10 x 10 | 10^{6} |

1,000 | 10 x 10 x 10 | 10^{3} |

100 | 10 x 10 | 10^{2} |

10 | 10 | 10^{1} |

1 | 10^{0} | |

0.1 or \(\frac{1}{10}\) | \(\frac{1}{10}\) | \(\frac{1}{10^1}\) or 10^{-1} |

0.01 or \(\frac{1}{100}\) | \(\frac{1}{100}\) or \(\frac{1}{10 \times 10}\) | \(\frac{1}{10^2}\) or 10^{-2} |

0.001 or \(\frac{1}{1000}\) | \(\frac{1}{1000}\) or \(\frac{1}{10 \times 10 \times 10}\) | \(\frac{1}{10^3}\) or 10^{-3} |

0.000001 or \(\frac{1}{1,000,000}\) | \(\frac{1}{10 \times 10 \times 10 \times 10 \times 10 \times 10}\) | \(\frac{1}{10^6}\) or 10^{-6} |

0.000000001 or \(\frac{1}{1,000,000,000}\) | \(\frac{1}{10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10}\) | \(\frac{1}{10^9}\) or 10^{-9} |

(click here for an image of the chart)

This Snack is based on an exploration originally developed by Margaret Till and Cynthia Surmacz of the Department of Biological and Allied Health Sciences at Bloomsburg University, Bloomsburg, Pennsylvania, to whom we give many thanks!