[size=150]In the applet below, 3 digits after the decimal for the decimal expansion of [math]\frac{3}{7}[/math] have been calculated. Find the next 4 digits.[/size]

[size=150]The cards show Noah’s work calculating the fraction representation of [math]0.4\overline{85}[/math]. Arrange these in order to see how he figured out that [math]0.4\overline{85}=\frac{481}{990}[/math] without needing a calculator.[br][br]Use Noah’s method to calculate the fraction representation of:[/size][br][br][math]0.1\overline{86}[/math]

[math]0.7\overline{88}[/math]

Use this technique to find fractional representations for [math]0.\overline{3}[/math] and[math]0.\overline{9}[/math].

Why is [math]\sqrt{2}[/math] between 1 and 2 on the number line?

Why is [math]\sqrt{2}[/math] between 1.4 and 1.5 on the number line?

How can you figure out an approximation for [math]\sqrt{2}[/math] accurate to 3 decimal places?

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, [math]C=2\pi r[/math]?

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, [math]C=2\pi r[/math]?

How can you explain the differences between these calculations of [math]\pi[/math]?