Question

which one of the following shows the numbers 3.3, 3.37, and $3\\ 1/5$ placed in the correct order, from small to large?
\bigcirc 3.3\quad 3.37\quad $3\\ 1/5$
\bigcirc $3\\ 1/5$\quad 3.3\quad 3.37
\bigcirc $3\\ 1/5$\quad 3.37\quad 3.3
\bigcirc 3.37\quad 3.3\quad $3\\ 1/5$
\bigcirc 3.37\quad $3\\ 1/5$\quad 3.3
\bigcirc 3.3\quad $3\\ 1/5$\quad 3.37

you need to change the mixed number $46\\ 2/9$ into a decimal number. which one of the following procedures should you do?
\bigcirc multiply 2 times 9 and then place 46 directly to the left of the decimal point.
\bigcirc multiply 46 times 9 and then place 2 directly to the left of the decimal point.
\bigcirc divide 46 by 9 and then place 2 directly to the left of the decimal point.
\bigcirc divide 2 by 9 and then place 46 directly to the left of the decimal point.

Explanation:

Step1: Convert fraction to decimal

$3\frac{1}{5} = 3 + \frac{1}{5} = 3 + 0.2 = 3.2$

Step2: Compare the three numbers

$3.2 < 3.3 < 3.37$, so the order is $3\frac{1}{5}, 3.3, 3.37$

Step3: Analyze mixed number conversion

A mixed number $a\frac{b}{c}$ converts to decimal by $\frac{b}{c} + a$, so for $46\frac{2}{9}$, divide 2 by 9, then place 46 left of decimal.

Answer:

1. $3\frac{1}{5}$ 3.3 3.37
2. Divide 2 by 9 and then place 46 directly to the left of the decimal point.