4-page entry…

Seed Questions:What is the area of a 3 cm by 4cm rectangle?

Exploration: Write kind of small.

The knee jerk mathematical answer to the SQ is ______.

But is this the best answer?

How well do we know this answer?

Suppose that the sides of this rectangle were only measured to the nearest centimeter.
What is the smallest this area could actually be, if you rounded the side measurements to 3cm by 4 cm starting with 2 sig figs?Hint: one side could be 2.5 cm.Show calc.

What is the largest this area could actually be?Show calc.

The range of possible areas is:

What is the single, most honestnumerical value for the area?

But isn’t 12 cm2more accurate?

Second page…
Let’s make this a matter of life and death. Youare trapped in a submarine resting on the bottom of a freshwater bay. The density of water around your sub is 0.998 g/cm3. You want to release something with the sub’s name on it that will float, to aid in your rescue. You happen to have a hollow metal block that has a mass of 39.85 g. You use a centimeter stick as shown to get the dimensions. Record the dimensions to 1 sig fig. Paste these photos into your PJ.

Do you expect your block will sink or float?Begin with all the numbers your calculator gives you, then round appropriately.

Sounds like you need more precise measurements. Here they are. Record the dimensions to 2 sig figs. Again, paste photos into your PJ.

Calculate the volume and the density.

Now do you expect your block will sink or float?Again, begin with all the numbers your calculator gives you, then round appropriately.

Third page…

What? You want more precision? OK.Here it is. Record the caliper dimensions to 3 sig figs. Paste these images too.

Calculate the volume and the density again.

What do you conclude about whether your block will sink or float?Again, begin with all the numbers your calculator gives you, then round appropriately.

Fourth page…

Time to test your conclusion above. Did your block sink or float?

Big Idea:Sig figs can save you time, money, and maybe your life.

There are 3 types of numerical values:

Type / How well do you know it? / # of Sig Figs
Measured Quantities: / Approximately / Number varies
Defined Quantities: / Exactly / Infinite
Integer Counting: / Exactly / Infinite s

Product/Quotient Rule: Go with the least number of sig figs in a product or quotient.

Example: 2.0 ÷ 3 = 0.7 (1 sig fig in answer)

Addition/Subtraction Rule: Line up the decimal places.

Example: 25 – 0.3 = 25.?

- 0.3

25.? → = 25

It is best to avoid interim rounding: round to the appropriate sig figs at the end:

(25 – 1.6) 2.455 = (23.4)(2.455)

= (57.447) → = 57

Discussion: