Powers of 10, Einstein's Equivalence

How many years are there in a billion seconds?

In other words, 1,000,000,000 seconds = how many years? You divide the seconds by 60 to get the equivalent number of minutes, then divide the result by 60 to get the hours, divide again by 24 to get the days, and finally divide the days by 365 (we don’t the precision of leap years in this estimate) to get the required number of years.
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1 billion seconds is approximately equal to 31.69 years.

How to put this in perspective? If you consider 2 billion seconds, that’s about 63 years, the longevity of people in many countries of the world today, reflecting the advances in medicine.

Power of 10 translate to order of magnitude estimation. Usually we say that if a number x is 10 times greater than another number y, then x is one order of magnitude higher than y. To be able to calculate order of magnitude estimation in comparing numbers, especially numbers that have some relevance to life, is a valuable skill to have. If a city is hit by an earthquake that measures 8 on the Richter scale and another city by 6, we say that the former was hit by an earthquake that is 10 to the power of 2 = 100 times more powerful than the latter. The order of magnitude is this case is 2. The Richter scale is a logarithmic scale, and so the difference of 2 (8 - 6) in this case is the order of magnitude.

So, they are all related - powers of 10, order of magnitude and the logarithmic scale.
What's a trillion dollar $1,000,000,000,000 like? The number is so big but that it eludes the human mind. On the other hand, ask this question: If you were to stack up $100 bills, how high would a trillion dollars reach? (Try to estimate the answer. There are also visually exciting YouTube videos!)

These are fun math to do but they also illustrate an important idea: sometimes connections between numbers and visualizing them by relating them to life are more important than the numbers themselves.
The unit of brain power is often measured in synapse. How many synapses are there is the human brain? 1, followed by 15 0's. It's thousand trillion!

And how long is our sun expected to shine before it uses up its raw material of hydrogen? 10 to the power of 17 seconds. That’s about 5 billion years. The sun has already been shining for about 5 billion years, so we are halfway through its life already. But 5 billion years is still a long way to go.

If we use Einstein’s famous energy-mass conversion formula E = mc2, where m is the mass and c is the velocity of light, it means that a tiny mass contains a huge amount of energy.

Mass from the sun (hydrogen fusing into helium) radiates as light that warms the earth 93 million miles away. There is enough fuel in the sun to keep us, and our descendants through many, many generations, warm for 5 billion years more. How much mass of the sun is converted to energy that strikes the earth every second? Only 4 pounds, or 64 ounces, at 16 ounces to a pound. For perspective, consider this: If we could convert the entire mass of a typical walnut (about 1 ounce) into energy, it could power a small city for years!

Please contact me if you and your employees want to acquire numerical and statistical skills to make sense of the numbers and the data that surround us. Tools required: paper and pen, and an open mind!