# Scientific Conversions

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## Objective

SWBAT write, compare, and solve problems using decimals in scientific notation.

#### Big Idea

Many numbers in the sciences are just too large or too small to write. Scientific Notation sizes them down.

## LAUNCH

12 minutes

To begin the lesson I project an image of Jupiter and Earth on the board. The size difference between the planets draws student's attention, so it's a good way of starting. This lesson works well with student pairs so I quickly randomly pair them up. At first, both students will perform pencil-paper calculations to compare answers. Afterwards, one student can use the calculator while the other records data.

Once students are paired and while they are making comments about our earth's size compared to Jupiter's, I write on the board.

Find the Surface Area of Planet Jupiter

S.A. = 4πr2

Most of the students in the class will actually be surprised how small Earth is relative to Jupiter. I tell them to use the Surface Area formula and find their size without the use of a calculator.

Using 3.14 for pi, it should be relatively easy for students to calculate the surface area of Jupiter and obtain 61,544,000,000 kilometers. After a couple of minutes, I call on a student to say the number in words. I then do the same for Earth’s surface area (514,457,600 km).

Finally, I ask the class;  "How many times larger is the surface area of Jupiter?" I tell my stuents to make rough estimations by rounding the numbers. Students should find that Jupiter is about 120 times larger in surface area.

## NEW INFORMATION

12 minutes

Now I ask students to take out their calculators and use them to find each precise surface area.   I write what their screen will look like on the board.

6.1544x1010      or     6.1544 EE 10 depending on the calculator used.

I inform the students that the numbers are expressed in Scientific Notation, a shorthand way to write very large numbers (or very small numbers). Both calculator screen expressions are equivalent to 6.1544 ∙ 1010  Ask students to show their calculator screens to other students close to them so that everyone sees the two different versions of the number.

On the board, I write; “In scientific notation, a number greater than or equal to 1 and less than 10 is multiplied by an integer power of 10.”

Immediately write or project the NEW INFO EXPRESSIONS on the board and call on students to identify whether the expression is in scientific notation or not according to the statement above. If not, why not?

Then I instruct the class to find and write the surface area of the earth in scientific notation.

## APPLICATION

20 minutes

At this point, I hand each student the Scientific Notation Learning Sheet.  I encourage the students to continue to work and discuss their work in pairs.

For Questions 1 and 2

I do not immediately teach the process of converting numbers to scientific notation by having students learn to count places to the left or to the right. Rather, I help students to realize what happens when you multiply a number by a power of 10 with a positive or negative exponent.

In question 2, learners should see that in order to get such a small number they must multiply 5 by a negative power of 10, in other words, a fraction, which means they end up dividing by that power.

For Question 3 and 4

As students work I walk around monitoring their work. If students get stuck with Question 3, I ask students to first write 3.706. Then, I ask students to predict whether the exponent of the base 10 will be positive or negative. The answer to look for is that, since 370,600,000 is larger than 3.706,  the exponent of 10 must be positive. After acknowledging this, I ask students, "How many 3.706's do you have in that number?" This is a difficult question for students. The fallback strategy here is that students count the number of places, finding that in this case, the exponent is 8. I encourage students to express this The same kind of thought should go into answering Question 4. Again, I try and avoid students trying to "bottle" the thought of when to move the decimal to the right or left.

For Question 5

I encourage students to do Question 5 with pencil and paper and no calculators. Students should give an explanation that demonstrates understanding of the relation between the decimal part (coefficient) and the power. I tell the class that only one of the equivalent expressions is in true scientific notation. Students may ask why, if the other answers are correct, should we only use the one in scientific notation. I let learners know that there has to be common ground for communication purposes. Just like it's been decided what the international units of measurement are. The scientific and mathematics community uses this shorthand notation for consistency in communication.

Question 6

This question is one students will be able to answer in the next lesson. So, it is a kind of extension of this lesson on conversion. Since both surface areas have already been converted into scientific notation, students have a head start.

## CLOSURE

10 minutes

To end the lesson,  I hand pairs of students the LESSON CLOSURE Sci Not resource. The instructions are to order the surface areas (Sq.Km) of the planets from greatest to least. Students should be able to order these without the use of calculators and without showing any work.

I give the class a few minutes as I walk around seeing what criteria the students are using. Then I ask any of the pairs to state the planets in order from least to greatest and to inform the class how they managed. Students should state that....

Saturn was easily identified as the largest because of the highest power of 10....Mercury, the smallest, using the same reasoning. When having to decide between numbers with the same powers of ten, they simply checked the decimal or first part of the scientific notation value and compare these.

CORRECT ORDER

Saturn         4.27 x 1010  sq. km.

Uranus        8.1156 x 109   sq. km

Neptune       7.6408 x 109  sq. km

Venus          4.60 x 108  sq. km.

Mars            1.44798465 x 108 sq. km

Mercury       7.48 x 107  sq. km