Question

round 0.446 kilometer to the nearest tenth by following these steps:
a. complete the marking of the number line to show hundredths.
b. label 0.446 on the number line.
c. determine whether 0.446 is closer to 0.4 or 0.5. if the hundredths digit in 0.446 is 5 or greater, round up. if the hundredths digit in 0.446 is less than 5, round down. what is 0.446 kilometer rounded to the nearest tenth?

Answer:

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<reasoning>

Identify the given values and goals

We are given the decimal number \(0.446\) representing a distance in kilometers.
The goal is to round \(0.446\) to the nearest tenth by completing three tasks:

• a. Complete the marking of the number line to show hundredths.
• b. Label \(0.446\) on the number line.
• c. Determine whether \(0.446\) is closer to \(0.4\) or \(0.5\), and round it to the nearest tenth using the rounding rule.

Complete the number line markings

Using Decimal Place Value and Visualizing Decimals, we analyze the number line.
The main marked points are \(0.40\), \(0.45\), and \(0.50\).
There are 5 intervals between \(0.40\) and \(0.45\), meaning each tick mark represents \(0.01\) (one hundredth).
The tick marks from left to right are:

• \(0.40\)
• \(0.41\)
• \(0.42\)
• \(0.43\)
• \(0.44\)
• \(0.45\)
• \(0.46\)
• \(0.47\)
• \(0.48\)
• \(0.49\)
• \(0.50\)

Label 0.446 on the number line

The number \(0.446\) lies between \(0.44\) and \(0.45\).
Since \(0.446\) is slightly more than halfway between \(0.44\) and \(0.45\), we place the label just to the right of the midpoint between the fourth tick mark (\(0.44\)) and the fifth tick mark (\(0.45\)).

Determine closeness and round

We compare the distance from \(0.446\) to \(0.4\) and \(0.5\):

• Distance to \(0.4\): \(0.446 - 0.400 = 0.046\)
• Distance to \(0.5\): \(0.500 - 0.446 = 0.054\)

Thus, \(0.446\) is closer to \(0.4\).

Using the rounding rule:
The hundredths digit of \(0.446\) is \(4\).
Since \(4 < 5\), we round down.
Therefore, \(0.446\) rounded to the nearest tenth is \(0.4\).
</reasoning>

<answer>

Question a

The completed tick marks from left to right are:
\(0.40\), \(0.41\), \(0.42\), \(0.43\), \(0.44\), \(0.45\), \(0.46\), \(0.47\), \(0.48\), \(0.49\), \(0.50\).

Question b

The label for \(0.446\) is located between the tick marks for \(0.44\) and \(0.45\), slightly past the halfway point toward \(0.45\).

Question c

• \(0.446\) is closer to \(0.4\).
• The hundredths digit in \(0.446\) is \(4\), which is less than \(5\), so we round down.
• \(0.446\) kilometer rounded to the nearest tenth is \(0.4\) kilometer.

</answer>

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"size": 4,
"color": "#F2557F",
"withLabel": true,
"labelPosition": [0.446, 0.5]
}
}
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