Question

plot, order, and compare decimals

1. four students volunteered at the animal shelter and recorded their hours on the chart.

volunteer hours
kayla: 3.45 hours
erin: 3 + 0.05 hours
matt: 3.249 hours
thomas: three and six tenths hours
part a
plot and label the students hours on the number line.
number line with marks at 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 and label time spent volunteering (in hours)
part b
order their volunteer hours from least to greatest.
four rectangles labeled least (first) and greatest (fourth)
part c
use standard form and <,>,= to compare two students volunteer hours.
two rectangles and a circle for the symbol
part d
matt says that he has completed the most volunteer hours because he has the most digits. explain matt’s error.
three lines for writing the explanation

Explanation:

Part A

• Kayla: \(3.45\) is between \(3.4\) and \(3.5\).
• Erin: \(3 + 0.05=3.05\) is between \(3.0\) and \(3.1\).
• Matt: \(3.249\) is between \(3.2\) and \(3.3\).
• Thomas: Three and six - tenths is \(3.6\).

Part B

• First, compare the whole number parts (all are \(3\)).
• Then, compare the tenths place:
• Erin (\(3.05\)) has a tenths digit of \(0\).
• Matt (\(3.249\)) has a tenths digit of \(2\).
• Kayla (\(3.45\)) has a tenths digit of \(4\).
• Thomas (\(3.6\)) has a tenths digit of \(6\).
• So the order from least to greatest is: Erin (\(3.05\)), Matt (\(3.249\)), Kayla (\(3.45\)), Thomas (\(3.6\)).

Part C

• For example: Erin (\(3.05\)) and Matt (\(3.249\)). Since \(3.05<3.249\).

Part D

• When comparing decimals, we look at the value of each digit based on its place - value (tenths, hundredths, thousandths etc.), not the number of digits. For example, \(3.05\) has two digits after the decimal, \(3.249\) has three digits after the decimal, but \(3.05 < 3.249\) because when we compare the tenths place \(0<2\).

Answer:

• Part B: Erin (\(3.05\)), Matt (\(3.249\)), Kayla (\(3.45\)), Thomas (\(3.6\))
• Part C: Example: \(3.05<3.249\) (Erin < Matt)
• Part D: When comparing decimals, we look at the value of each digit based on its place - value (tenths, hundredths, thousandths etc.), not the number of digits. For example, \(3.05\) has two digits after the decimal, \(3.249\) has three digits after the decimal, but \(3.05 < 3.249\) because when we compare the tenths place \(0<2\).