Category: Numbers

Number Sense – Activity: Tsunami Numbers in the News

About a decade ago, there was a great Tsunami happening in Asia.
What do you know about the Asian tsunami?

Read through the article first. Use the following numbers to fill in the blanks in the story.Think about which numbers make sense.

500  20  8,000;  2004  110,000  30,000  9.0

A tsunami triggered by a very large earthquake off the coast of the
Indonesian island of Sumatra on December 26, ____, has left
more than 150,000 people dead and millions homeless. Countries hit hardest by the disaster include
Sri Lanka, Indonesia, India, Thailand, and the Maldives. Almost 75% of the deaths occurred in
Indonesia, estimated at ____. Sir Lanka was second highest with about 20% of the estimated deaths, or
______ people lost that day. The rest of the deaths, approximately ____, occurred in the other nine
countries affected by the tsunami.
The ____ foot wall of water, higher than a two-story building,
swallowed entire villages. The tsunami waves were not only very high, they moved at a much faster speed
than normal. These waves were comparable in size to those you see on some of the surfing movies;
but those waves travel at 30 miles an hour, and the tsunami waves
were moving more than fifteen times as fast at ____ miles an hour.
The velocity of the force is what caused the destruction—a massive force that swept away everything in its path.

The earthquake causing this Tsunami was a destructive earthquake measuring ______ on the Richter scale,
the fourth worst earthquake in recorded history. Earthquakes are measured on a Richter scale that has
a range from 0 to 12; a 6.0 on the scale is a pretty bad earthquake.

(Story constructed from January 2005 news reports)

Complete Numbers in Fraction Equations

The formula on our face page of “amazing numbers” is rather interesting:
1 – (1 ⁄ 28) = (1 ⁄ 2) + (1 ⁄ 4) + (1 ⁄ 7) + (1 ⁄ 14)

The point of interest is that: if you look at all divisors of 28: they are 1,2,4,7,14,28; with the exception of 28 which is itself, all divisors have appeared in this formula, and they appear in the form of so-called “unit fraction”, where numerator is 1. So (1 ⁄ 2), (1 ⁄ 4), etc. are all unit fractions.

Indeed, we present a fraction equation to make it a bit unusual, but there is a low-pitch but straightforward ways to present number 28. We have that:
28 = 1 + 2 + 4 + 7 + 14
To get to the earlier fraction form, just divide every term by the number 28.

The smallest complete number is 6 (=1+2+3), 28 is the 2nd complete number, and after that, you will not see a complete number until 496. So complete numbers are rare among all positive whole numbers.

Complete numbers 6 also has a nice fraction form, as:
1 – (1⁄6) = (1⁄2) + (1⁄3)

Prime numbers

Prime numbers are those that have 1 (one) and itself as the only two divisors. Examples of primes are 2, 3, 5, 7, 11. None of 4, 6, 9 is a prime since 4 = 2 × 2, 6 = 2 × 3, and 9 = 3 × 3.

If a number greater than one is not a prime, then it is a composite number, and can be factored into the product of primes — called prime factorization. We have given the prime factorization of 4, 6, 9 as above. For a couple of more examples:

12 = 2 × 2 × 3

36 = 2 × 3 × 3 × 3

28 = 2 × 2 × 7

So all natural numbers are divided into three classes: the number 1, the prime numbers, and the composite numbers.

A bonus point: π, besides representing in a circle, the ratio of circumference to diameter, also stands for a special function related to prime numbers. Function π(x) — for every integer x, represent the number of primes less than or equal (i.e. not exceeding) x. For example, we have:

π(2) = 1, π(3) = 2, π(10) = 4, π(20) = 8 etc.
[To find why π(10) = 4, recall the 4 prime numbers not exceeding 10: they are 2,3,5, and 7.]