Powers of Ten: From 10^0 to 10^24 (Astronomy) back to 10^-16 (Microscopy)

After introducing the children to exponents with the Target Number and 24 Game over the last three weeks, we entered into the most exciting powers in math: Powers of Ten.



First, they found a pattern in 10^nth and the number of zeros that follow the one. For example, 10^3 is a 1 followed by 3 zeros = 1000. See the table of solutions on page 2 of each pdf.


Second, we looked at the difference between the metric system and the imperial or customary system of numbers. The latter is used by only 5% of the worlds population. I taught the children to use their fore finger middle knuckle to approximate one inch or about 2.5 centimeters. They all seemed to agree that metric makes so much more sense. See page 4 of each pdf.


Third, we looked at the names for each power of ten on page 5 of the pdfs and the children noticed a pattern of a sideways parabola formed by the zeros.


Fourth, I took them on a journey through space from 10^0 = 1 meter above an object and increasing by one power of ten each ten seconds until 10^24 100 million light years away from Earth and then back again until 10^-16 inside the atomic structure of a carbon atom. We journeyed through 40 powers of ten with a visual representation of each power. It is so difficult to comprehend the power of exponential growth of 900% and decay of 90%.


Here is a transcript of the video I shared and annotated for them. The link to this famous video is below.


I hope they come up with a million million questions.


  • Powers of Ten - Charles Eames for IBM 1977:     https://www.youtube.com/watch?v=0fKBhvDjuy0


  • Ten to the zeroth power meters (one meter): The picnic near the lakeside in Chicago was the start of a lazy afternoon early one October. It begins with a scene one meter wide which we view from just one meter away. 


  • Now every ten seconds we will look from ten times farther away and our field of view will be ten times wider. 


  • Ten to the first, this square is (ten meters wide) and in ten seconds the next square will be ten times as wide. Our picture will centre on the picnickers even after they've been lost to sight. 


  • Ten to the second, (one hundred meters wide), the distance a man can run in ten seconds, cars crowd the highway, power boats lie at their docks, the colorful bleachers are Soldier Field. 


  • At Ten to the third meters, this square is a kilometer wide, (one thousand meters), the distance a racing car can travel in ten seconds. We see the Great City on the lake shore. 


  • Ten to the fourth meters (10,000 meters), ten kilometers, the distance a supersonic airplane can travel in ten seconds. We see first around and the end of Lake Michigan, then the whole Great Lake. 


  • Ten to the fifth meters (100,000 meters), the distance a hovering satellite covers in ten seconds, long parades of clouds, the day's weather in the Mid-West. 


  • Ten to the sixth (1,000,000 meters), a one with six zeros. Soon the Earth will show as a solid sphere. We are able to see the whole Earth now, just over a minute along the journey. 


  • Ten to the seventh (10,000,000 meters), the Earth diminishes into the distance but those background stars are so much farther away that they do not yet appear to move. 


  • Ten to the eighth (100,000,000 meters), a line extends at the true speed of light. In one second, it half crosses the tilted orbit of the moon. 


  • Ten to the ninth (1,000,000,000 meters), you can start to see the path of the Earth's orbit about the Sun.


  • Ten to the tenth (10,000,000,000 meters), now we mark a smaller part of the path in which the Earth moves about the Sun. 


  • Ten to the eleventh (100,000,000,000 meters), now the orbital path of the neighbor planets, Venus and Mars then Mercury. 


  • Ten to the twelfth (1,000,000,000,000 meters), entering our field of view is the glowing centre of our solar system – the Sun, , followed by the massive outer planets, swinging wide in their big orbits. 


  • Ten to the thirteenth (10,000,000,000,000 meters), that aureole belongs to Pluto. A fringe of a million comets too faint to see completes the solar system. 


  • Ten to the fourteenth (100,000,000,000,000 meters), as the solar system shrinks to one bright point in the distance, our Sun is plainly now only one among the stars. 


  • Ten to the fifteenth (1,000 light years), looking back from here we note four southern constellations, still much as they appear from the far side of the Earth. 


  • This square is ten to the sixteenth meters (1 light year), not yet out to the next star, our last ten-second step took us ten light years further, the next will be a hundred. 


  • Ten to the seventeenth (10 light years), our perspective changes so much at each step now that even the background stars will appear to converge. 


  • Ten to the eighteenth (100 light years), at last we pass the bright star Arcturus and some stars of the Dipper. Normal but quite unfamiliar, stars and clouds of gas surround us as we traverse the milky way galaxy. 


  • Ten to the nineteenth (1,000 light years), giant steps carry us into the outskirts of the galaxy and as we pull away at 


  • Ten to the 20th (10,000 light years), we begin to see the great flat spiral facing us. The time and path we chose to leave Chicago has brought us out of the galaxy along a course nearly perpendicular to its disk.


  • Ten to the 21st (100,000 light years), the two little satellite galaxies of our own are the clouds of Magellan. 


  • Ten to the 22nd power, (1 million light years), groups of galaxies bring a new level of structure to the scene. 


  • Ten to the 23rd (10 million light years), glowing points are no longer single stars but whole galaxies of stars, seen as one. 


  • Ten to the 24th (100 million light years), we pass a big vulgar cluster of galaxies among many others, a hundred million light years out. As we approach the limit of our vision, we pause to start back home. This lonely scene, the galaxies like dust, is what most of space looks like. This emptiness is normal. The richness of our own neighbourhood is the exception. 


  • PART 2 The trip back to the picnic on the lake front will be a sped up version, reducing the distance to the Earth surface by one power of ten every two seconds. In each two seconds we will appear to cover 90% of the remaining distance back to Earth, noticing alternation between great activity and relative inactivity. A rhythm that will continue all the way to our next goal, a proton and nucleus of a carbon atom beneath the skin on the hand of the sleeping man at the picnic. Ten to the ninth meters, ten to the eighth, seven, six, five, four, three, two, one. We are back at our starting point. 


  • We slow up at one meter (100 Centimeters = 1 Meter). Ten to the zeroth power. Now we reduce the distance to our final destination by 90% every ten seconds. 


  • Ten to the negative one power (10 Centimeters): Each step much smaller than the one before. 


  • At ten to the negative second (10 Millimeters = 1 Centimeter), one hundredth of the meter, one centimeter, we approach the surface of the hand. 


  • Ten to the negative third (1000 Microns = 1 Millimeter): we will be entering the skin, crossing layer after layer from the outermost dead cells into a tiny blood vessel within. 


  • Ten to the negative fourth(100 Microns): Skin layers vanish in turn and outer layers of cells, Felty collagen, a capillary containing red blood cells and a roughly lymphocyte. 


  • Ten to the negative fifth (10 Microns): We enter the white cell, among its vital organelles, the porous wall of the cell nucleus appears. 


  • Ten to the negative sixth (1 Micron): The nucleus within holds the reality of the man in a coiled coils of DNA. 


  • Ten to the negative seventh(1000 ångstroms) : As we close in, we come to the double helix itself, a molecule like a long twisted ladder whose runs of paired bases spell out twice - in an alphabet of four letter, the words of a powerful genetic message. 


  • Ten to the negative eighth (100 ångstroms): At the atomic scale, the interplay of four electrons in motion becomes more visible. 


  • Ten to the negative ninth (10 ångstroms): We focus on on one commonplace group of three hydrogen atoms bonded by electrical forces to a carbon atom. Four electrons make up the outer shell of the carbon itself. They appear in quantum motion as a swarm of shimmering points. 


  • At ten to the minus ten meters, (1 ångstrom), we find ourselves right among those outer electrons. Now we come upon the two inner electrons held in a tighter swarm. 


  • Ten to the negative eleventh (.1 Angstroms): As we draw toward the atom's attracting centre, we enter upon a vast inner space. 


  • Ten to the negative twelfth (.01 Angstroms): At last the carbon nucleus. So massive and so small. This carbon nucleus is made up of six protons and six neutrons. 


  • Ten to the negative thirteenth (.001 Angstroms): We are in the domain of universal modules. There are protons and neutrons in every nucleus. Electrons in every atom. Atoms bonded to every molecule out of the farthest galaxy. 


  • Ten to the negative 14th (.0001 Angstroms): As a single proton fills our scene we reach the edge of present understanding. 


  • Ten to the negative 15th (.0001 Angstroms): Are these some quarks of intense interaction? 


  • Ten to the negative 16th (.00001 Angstroms): Our journey has taken us through forty powers of ten. If now the field is one unit, then when we saw many clusters of galaxies together, it was ten to the fortieth or one and forty zeros.



330pm_Powers_of_Ten.pdf4.72 MB
430pm_Powers_of_Ten.pdf8.35 MB
530pm_Powers_of_Ten.pdf5.43 MB