# A discussion of numbers in real life

What is the use of scientific notation in every day life? Scientific notation is needed any time you need to express a number that is very big or very small.

Suppose for example you wanted to figure out how many drops of water were in a river 12 km long, 270 m wide, and 38 m deep assuming one drop is one millilitre. It's much more compact and meaningful to write the answer as roughly than it is to write 123120000000000. For one thing, the scientific notation is easier to read, and makes it much easier to tell at a glance what the order of magnitude is rather than counting zeros.

For another, most of the digits in 123120000000000 are completely meaningless unless your measurements were very precise. For instance, if the exact river length were really 12. So it's better to use a notation like scientific notation in which you can suppress the inaccurate digits.

## Scientific Notation in Everyday Life

Followup question by an anonymous poster on February 11, 1997: Who created scientific notation? What are the uses for it in the work field?

- So there are 5 people in each team;
- Sometime between then and the present it became common to write large and small numbers that way, as well as numbers where it's important to convey an indication of the precision of a measurement; I do not know when it became common practice or who started doing it, but I will see if I can find out;
- Suppose for example you wanted to figure out how many drops of water were in a river 12 km long, 270 m wide, and 38 m deep assuming one drop is one millilitre;
- Especially point out stories that differ in logical structure More About Construction of Number Sentences , not just context.

Scientific notation was not "created", in the sense of someone coming up with something new. The fact that happens to equal 30000 is a mathematical truth, not a creation.

## The Uses of Numbers in Our Daily Life

The question becomes, though, when did it become commonplace to write the first form instead of the second form. I do not know who first used scientific notation. The concept would be very old; you'd have to dig back to the first time someone thought of describing 10000000000 as "a one followed by ten zeros", realized that's the same asand wrote it that way in whatever notation they were used to using for exponents.

- Note that there are a lot of correct answers;
- Students can begin to use brackets by circling the operation to be completed first, then reducing the circling to brackets;
- An apple costs 45 cents, and a mandarin costs 25 cents;
- In each case, students should write the number sentence as part of the solution;
- For each number sentence, students write one or more story problems, and draw or show a visual model.

The modern notation for exponents writing them raised at a higher level originated with Descartes in 1637, so you would never have seen an expression like before then.

Sometime between then and the present it became common to write large and small numbers that way, as well as numbers where it's important to convey an indication of the precision of a measurement; I do not know when it became common practice or who started doing it, but I will see if I can find out.

It most likely occurred during the 1800's and 1900's when scientists were developing their understanding of the astronomical universe involving really huge numbers to describe distancesand of the world of subatomic particules involving really small numbers.

I don't know that I can say in answer to the question "what are the uses for it in the work field", other than what I've already said in answer to the previous question on this page: For example, if you're an engineer and you want to record the pressure on a supporting beam of a bridge, and you measure it as 500034 but your instrument is only precise toyou would not want to write "500034" because you really have no way of knowing, based on your measurement, what the last few digits are.

## Construction of Number Sentences: Level 3

On the other hand, you wouldn't want to just round it to 500000, because that doesn't convey the fact that you do precisely know the first few digits! Scientific notation is the perfect way to express the number and give an idea of how precise it is.

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