Name ______
Date ______Period ______
Problem 3.3 – Decimal Benchmarks
Decimal Benchmarks
Below are representations of ¾ on a hundredths grid and on a number line.
Consider these questions:
Each representation shows that ¾ is 75 out of 100 parts.
How would you write this as a decimal?
Different representations are usually good for different things.
Which representation, the grid or the number line, do you
find most useful?
Sometimes knowing a little can go a long way! With
decimals and fractions, knowing just a few fractions and
their decimal equivalents can help you think about many
other fractions and their decimal equivalents. In Problem 3.3
you will make a list of benchmarks that show
equivalent fractions and decimals.
Mary wants to make a list of decimal benchmarks for these fraction
benchmarks:
1 1 1 1 1 1 1
2 3 4 5 6 8 10
A. 1. For which of Mary’s benchmark fractions do you already know
the decimal equivalent? Show how you know.
2. Use hundredths grids to find decimals that represent or are close
approximations for the ones you do not know.
3. Compare your decimals for ¼ and 1/8.
4. Compare your decimals for 1/3 and 1/6.
B. Use your work with Mary’s benchmark list to help you find decimal equivalents for the following groups of fractions:
1. 2 = 3 = 4 = 6 =
5 5 5 5
2. 2 = 3 = 4 = 5 =
8 8 8 8
6 = 7 =
5 5
3. 4 = 2 = 3 = 3 =
20 6 12 6
4. Describe strategies you used to find decimal equivalents.
C. Which fraction benchmark is each decimal nearest?
1. 0.18 2. 0.46
3. 0.225 4. 0.099
5. Describe one strategy you used to find your answers to
parts (1) – (4).
Name______HR#______
Problem 3.3
Applications
1. For parts (a) – (c), use number lines to show the given fractional
amount. Write the fraction as an equivalent decimal.
a. 20 b. 5 c. 13
25 8 26
2. Pilar divided 1 by 9 on her calculator and found that 1/9 was
approximately 0.1111. Find decimal approximations for each of the
following fractions.
a. 2 = b. 11 = c. 6 = d. 2 =
9 9 9 3
e. Describe any patterns that you see.
3. Ella says that she can find the decimal equivalent for lots of fractions
because she knows that the decimal equivalent for 1/5 is 0.2. Name
three fractions for which Ella could find the decimal equivalent. Explain
how Ella would use 1/5 to find the decimal for each fraction.
4. Which fraction benchmark below is each decimal nearest?
1 1 1 1 1 1 1
2 3 4 5 6 8 10
a. 0.30 b. 0.50 c. 0.12333 d. 0.15
For exercises 5 – 10, find an estimate if you cannot find the exact answer. you may find that drawing a number line, a hundredths grid, or some other diagram is useful in solving the problem. Explain your reasoning.
5. What is ¼ of 12? 6. What is ¾ of 8?
7. What is 2/9 of 18? 8. What is 2/9 of 3?
9. What is ¼ of 3? 10. What is ¾ of 3?