CBP 3.4—Decimals on the Number Line
Name: ______________________________ Period: __
In Problem 3.3, you thought of a pan of lasagna that was cut into 100 pieces, and you considered
relationships between the fractional and decimal representations for different numbers of servings.
The place value chart below shows the names of each position relative to the decimal point.
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What do you notice about the fraction names of each place value as you move to the right from the
decimal point?
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Why are these names useful in writing fractions as decimals?
It is often useful to divide a whole number into more than 100 pieces. When working with decimals you
can always divide the whole into smaller pieces, but you must always use a divisor that is a power of 10.
For example, you made a tenths strip in Investigation 1. You can fold or mark the tenths strip to get a
hundredths strip.
Similarly, you saw the hundredths grid in Problem 3.3. If each square in a hundredths grid on the left is
divided into 10 pieces, you get a thousandths grid. If you divide each part of a thousandths grid on the right
into 10 pieces, you get a ten-thousandths grid.
How can you use decimal notation to write amounts such as 12 hundredths of a pan of lasagna?
A. 1. Use the number line and the tenths strip below. Which of the points , , and can you name using a
tenths strip?
A. 2. Use a hundredths strip to name the same points.
A. 3. Write each fraction above as a decimal. How does the hundredths strip help you to do this?
B. 1. a. Which of the fractions below could be written with tenths or hundredths in the denominator? For
each such fraction, write an equivalent decimal.
B. 1. b. Which fractions cannot be written with tenths or hundredths in the denominator? Why not?
B.2. Name two other fractions that are easy to write as equivalent decimals.
Name two other fractions that are NOT easy to write as equivalent decimals.
Explain.
B. 3. a. Which decimal is closest to ?
Explain.
a. 0.3
b. 0.33
c. 0.333
B. 3. b. Are any of the decimals above exactly ? Explain.
C. Find decimal equivalents for each group of fractions.
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Describe the strategies you used to find them.
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