Question

1. what is similar about your answers to the previous question? what is different?
2. use the decimal representations to decide which of these fractions has the greater value. explain your reasoning.

are you ready for more?
one common approximation for ( pi ) is ( \frac{22}{7} ). express this fraction as a decimal. how does this approximation compare to 3.14?

Explanation:

Step1: Divide 22 by 7

To convert the fraction $\frac{22}{7}$ to a decimal, we perform the division: $22 \div 7$.
We know that $7\times3 = 21$, so $22\div7 = 3 + \frac{1}{7}$. Now, $\frac{1}{7} \approx 0.142857$. So, $22\div7 \approx 3.142857$.

Step2: Compare with 3.14

Now, we compare $3.142857$ (the decimal form of $\frac{22}{7}$) with $3.14$.
We can see that $3.142857>3.14$ because the third decimal place of $3.142857$ is $2$ and the third decimal place of $3.14$ (which can be written as $3.140000$) is $0$, and $2 > 0$.

Answer:

The fraction $\frac{22}{7}$ as a decimal is approximately $3.142857$. This approximation is greater than $3.14$ because $3.142857$ has a non - zero digit in the thousandths place (and beyond) while $3.14$ has zeros in those places, and $3.142857 - 3.14=0.002857>0$.