Powers of TenPowers of TenVsVs

Scientific NotationScientific Notation

How to tell the difference.How to tell the difference.

Powers of TenPowers of Ten

Why do we need to know this? Why do we need to know this? It is important to understand how we can It is important to understand how we can

express numbers that are VERY large or express numbers that are VERY large or VERY small.VERY small.

Some circuit boards – you know, those Some circuit boards – you know, those weird looking things on the backs of weird looking things on the backs of machines – have holes with diameters as machines – have holes with diameters as small as 10ˉ² or 0.01 of an inch. That is small as 10ˉ² or 0.01 of an inch. That is really, really small.really, really small.

A Circuit BoardA Circuit Board

Sometimes people actually paint on just the Sometimes people actually paint on just the head of a pin. They used a single hair to do head of a pin. They used a single hair to do the painting. Now the painting. Now thatthat is small. is small.

This personThis person painted on the hair itself! Do painted on the hair itself! Do you have that kind of patience?you have that kind of patience?

That is why we need ways to write smaller and That is why we need ways to write smaller and larger numbers without always having to use all larger numbers without always having to use all those zeros. those zeros. Below is a chart to show you the difference Below is a chart to show you the difference between positive and negative powers of ten.between positive and negative powers of ten.

What is the relationship between the positive What is the relationship between the positive powers of ten and the amount of zeros?powers of ten and the amount of zeros?What about the negative powers of ten?What about the negative powers of ten?

How can you multiply by a positive How can you multiply by a positive power of ten?power of ten?

How about dividing by a positive How about dividing by a positive power of ten?power of ten?

Let’s check out the negative Let’s check out the negative powers of ten.powers of ten.

We’ll start with multiplying.We’ll start with multiplying.

Now for dividing negative powers of Now for dividing negative powers of ten.ten.

Can we make this easier to Can we make this easier to remember? remember?

Sure…just copy this Sure…just copy this chart down in your chart down in your notes.notes.

Now you can use it to Now you can use it to study. study.

++positivepositive

--negativenegative

xx RR LL

÷÷ LL RR

Let’s try some problems with powers of ten. 3.18 x 10³ Answer: 3,180 106.9 ÷ 10³ Answer: .1069 6,387 ÷ 10 ˉ² Answer: 638,700 5.689 x 10 ˉ³ Answer: .005689

Now let’s look at Now let’s look at Scientific Notation!Scientific Notation!

Over the last 500 years, there have been Over the last 500 years, there have been many methods and devices used to many methods and devices used to calculate the speed of light. calculate the speed of light.

A scientist named Jean Bernard Leon A scientist named Jean Bernard Leon Foucault measured the different angles at Foucault measured the different angles at which light hit mirrors. which light hit mirrors.

Another scientist named Olaus Roemer Another scientist named Olaus Roemer observed the frequent eclipses of Jupiter’s observed the frequent eclipses of Jupiter’s moon, Io. moon, Io.

Light travels about 670,600,000 miles per Light travels about 670,600,000 miles per hour. Scientific notation is used to write hour. Scientific notation is used to write large and small numbers more easily. large and small numbers more easily.

A number written in scientific notation is A number written in scientific notation is expressed as a number that is greater expressed as a number that is greater than or equal to 1, but less than 10, than or equal to 1, but less than 10, multiplied by a power of ten.multiplied by a power of ten.

In other words…In other words…

In other words…(copy this for In other words…(copy this for notes)notes)

Move the decimal point until there is only a Move the decimal point until there is only a digit in the ones place.digit in the ones place.

Count the places you moved.Count the places you moved. If you moved left, it will be a positive power If you moved left, it will be a positive power

of ten.of ten. If you moved right, it will be a negative If you moved right, it will be a negative

power of 10.power of 10.

Now, let’s write these numbers Now, let’s write these numbers using Scientific Notation.using Scientific Notation.

0.0238410.023841 Step 1 - move the decimal so there is only a Step 1 - move the decimal so there is only a

digit in the ones place.digit in the ones place.

2.38412.3841 Step 2 – How many spaces did you move it?Step 2 – How many spaces did you move it? Answer: 2Answer: 2 Step 3 – Which way?Step 3 – Which way? Answer: RightAnswer: Right So what is the scientific notation?So what is the scientific notation? Answer: 2.2341 x 10 ˉ²Answer: 2.2341 x 10 ˉ²

Here are some more for you to try!

0.00940051 Answer: 9.40051 x 10ˉ³

728 Answer: 7.28 x 10²

0.06753 Answer: 6.753 x 10ˉ²