IM 8.8.15 Lesson: Infinite Decimal Expansions
In the applet below, 3 digits after the decimal for the decimal expansion of have been calculated. Find the next 4 digits.
Here is a set of cards for your group. Each card will have a calculations side and an explanation side which you can see by clicking the cards.
The cards show Noah’s work calculating the fraction representation of . Arrange these in order to see how he figured out that without needing a calculator. Use Noah’s method to calculate the fraction representation of:
Use this technique to find fractional representations for and.
Why is between 1 and 2 on the number line?
Why is between 1.4 and 1.5 on the number line?
How can you figure out an approximation for accurate to 3 decimal places?
Label all of the tick marks. Make sure to add arrows from the second to the third number lines.
Elena notices a beaker in science class says it has a diameter of 9 cm and measures its circumference to be 28.3 cm. What value do you get for using these values and the equation for circumference, ?
Diego learned that one of the space shuttle fuel tanks had a diameter of 840 cm and a circumference of 2,639 cm. What value do you get for using these values and the equation for circumference, ?
Label all of the tick marks on the number lines. Use a calculator to get a very accurate approximation of pi and plot that number on all three number lines.
How can you explain the differences between these calculations of ?