Math Snap

STEP 1

Assumptions1. The cards contain the following numbers $\pi$, $3 . \overline{1}$, $\sqrt{3}$, $\frac{4}{5}$.
. We need to arrange these numbers from least to greatest.

STEP 2

First, we need to convert all numbers to a common form to compare them. The easiest way is to convert all numbers to decimal form.

STEP 3

Convert $\pi$ to decimal form. We know that $\pi$ is approximately3.1416.

STEP 4

Convert $3 . \overline{1}$ to decimal form. The overline indicates that the digit(s) under it repeat indefinitely, so this number is3.1111...

STEP 5

Convert $2 \sqrt{3}$ to decimal form. We know that $\sqrt{3}$ is approximately1.732, so $2 \sqrt{3}$ is approximately3.464.

STEP 6

Convert $2 \frac{4}{5}$ to decimal form. This is a mixed number, so we can convert it by adding the whole number to the fraction. $\frac{4}{5}$ is0.8, so $2 \frac{4}{5}$ is2.8.

STEP 7

Now we have all the numbers in decimal form $\pi$ is3.1416, $3 . \overline{1}$ is3.1111..., $2 \sqrt{3}$ is3.464, and $2 \frac{4}{5}$ is2..

STEP 8

Now we can compare these numbers and arrange them from least to greatest. The smallest number is $2 \frac{4}{5}$ (2.8).

STEP 9

The next smallest number is $\pi$ (3.1416).

STEP 10

The next smallest number is $3 . \overline{}$ (3.111...).

The largest number is $\sqrt{3}$ (3.464).
So, Kyoko should arrange the cards in the following order $\frac{4}{5}$, $\pi$, $3 . \overline{}$, $\sqrt{3}$.