Remember that $< $ means 'less than.'

• First, we compare $6$ and $5.99$ using a place value chart.

  ones		tenths	hundredths
  $\color{blue}6$	.	$0$	$0$
  $\color{red}5$	.	$9$	$9$

  Comparing place values from left to right, we see that in the ones place, the digit $\color{blue}6$ is greater than the digit $\color{red}5.$ Therefore, \[{\color{red}5}.99< {\color{blue}6}\] So, statement I is false.

• Next, we compare $6$ and $6.01$ using a place value chart.

  ones		tenths	hundredths
  $6$	.	$0$	$\color{red}0$
  $6$	.	$0$	$\color{blue}1$

  Comparing place values from left to right, we see that in the ones and tenths place, the digits are the same for both numbers. In the hundredths place the digit $\color{red}0$ is less than the digit $\color{blue}1.$ Therefore, \[6.0{\color{red}0}< 6.0{\color{blue}{1}}\] So, statement II is true.

• Finally, we compare $6$ and $7.15$ using a place value chart.

  ones		tenths	hundredths
  $\color{red}6$	.	$0$	$0$
  $\color{blue}7$	.	$1$	$5$

  Comparing place values from left to right, we see that in the ones place, the digit ${\color{red}6}$ is less than the digit ${\color{blue}7}.$ Therefore, \[{\color{red}6}< {\color{blue}7}.15\] So, statement III is true.

Remember that $>$ means 'greater than.'

• First, we compare $9.2$ and $9$ using a place value chart.

  ones		tenths
  $9$	.	$\color{blue}2$
  $9$	.	$\color{red}0$

  Comparing place values from left to right, we see that the digit in the ones place is the same for both numbers. Moving onto the tenths place, we see that the digit $\color{blue}2$ is greater than the digit $\color{red}0.$ Therefore, \[9.{\color{blue}2} > 9\] So, statement I is true.

• Next, we compare $9.2$ and $6.2$ using a place value chart.

  ones		tenths
  $\color{blue}9$	.	$2$
  $\color{red}6$	.	$2$

  Comparing place values from left to right, we see that in the ones place, the digit $\color{blue}9$ is greater than the digit $\color{red}6.$ Therefore, \[{\color{blue}9}.2 > {\color{red}{6}}.2\] So, statement II is true.

• Finally, we compare $9.2$ and $9.02$ using a place value chart.

  ones		tenths	hundredths
  $9$	.	$\color{blue}2$	$0$
  $9$	.	$\color{red}0$	$2$

  Comparing place values from left to right, we see that the digit in the ones place is the same for both numbers. Moving onto the tenths place, we see that the digit ${\color{blue}2}$ is greater than the digit ${\color{red}0}.$ Therefore, \[9.{\color{blue}2} > 9.{\color{red}0}2\] So, statement III is true.

Remember that $< $ means 'less than.'

Let's write down the place value charts for both numbers.

We now compare place values, going from left to right.

The digits in the ones and tenths places are the same for both numbers.

Moving on to the hundredths place, we see that the first number is less than the second if $\fbox{$\phantom{0}$}$ is less than ${\color{blue}4}.$

From the given answer choices, only $\color{red}2$ is less than ${\color{blue}4}.$

Using the 'less than' symbol, we can write

\[ 2.4{\color{red}{2}}7 < 2.4{\color{blue}{4}}6 \]

Remember that $< $ means 'less than.'

Let's write down the place value charts for both numbers.

We now compare place values, going from left to right.

The digits in the ones are the same for both numbers.

Moving on to the tenths place, we see that the first number is less than the second if $\fbox{$\phantom{0}$}$ is less than ${\color{blue}5}.$

From the given answer choices, only $\color{red}3$ is less than ${\color{blue}5}.$

Using the 'less than' symbol, we can write

\[ 4.{\color{red}{3}} < 4.{\color{blue}{5}} \]

Remember that $> $ means 'greater than.'

Let's write down the place value charts for both numbers.

We now compare place values, going from left to right.

The digits in the ones are the same for both numbers.

Moving on to the tenths place, we see that the first number is greater than the second if $\color{blue}4$ is greater than $\fbox{$\phantom{0}$}.$

From the given answer choices, $\color{blue}4$ is only greater than ${\color{red}2}.$

Using the 'greater than' symbol, we can write

\[ 0.{\color{blue}{4}} > 0.{\color{red}{2}} \]

Remember that $> $ means 'greater than.'

Let's write down the place value charts for both numbers.

We now compare place values, going from left to right.

The digits in the ones and tenths places are the same for both numbers.

Moving on to the hundredths place, we see that the first number is greater than the second if $\color{blue}3$ is greater than $\fbox{$\phantom{0}$}.$

From the given answer choices, only $\color{blue}3$ is greater than ${\color{red}0}.$

Using the 'less than' symbol, we can write

\[ 8.2{\color{blue}{3}} > 8.2{\color{red}{0}} \]

We write down the qualifying time and the times made by the boys in a place value chart.

To qualify, the time must be less than $12$ seconds.

We now compare place values, going from left to right.

The digits in the tens place are the same for all the numbers. We then compare the digits in the ones place. For the time to be less than $12$ seconds, these digits must be less than ${\color{blue}2}.$

Hence, the times that qualify for the school's soccer team are $1{\color{red}1}.1$ and $1{\color{red}1}.83.$ Therefore, Sam and Jimmy qualified for the soccer team.

We write down all the averages in a place value chart.

We note that the digits in the ones place are the same for all numbers. For the tenths place, the largest digit in this position is ${\color{blue}4}.$

Hence, $0.{\color{blue}4}01$ is the highest batting average. So, Laura has the highest batting average.