What we learned from the EMLA about students mistakes when working with decimals:
1. When asked to round to the nearest hundredth, many students chose thousandths. In the example
that follows many students would choose 2.170
Round 2.172 to the nearest hundredth
2.17
2.18
2.170
They may be confusing hundredth with hundreds, knowing that a number in the hundreds has 3
decimal places.
2. What is the best estimate of 41 + 3.77+ 79 + 0.23
When asked to estimate a sum or difference that involves decimals many students
 ignore the decimal and think of the numbers as all whole numbers or all decimals
 do rounding and then calculations without looking at the problem for such things as
compatible numbers (.77 and .23)
 add the actual numbers and then give an estimate that is close.
3. When presented with a problem like 3 189.06 with the following choices for answers
6302
630.2
63.02
6.302
a significant number chose the correct answer of 63.02 but a lot chose 630.2, indicating they could not
handle dividing the 3 into zero. Those that chose 6302 were ignoring the decimals.
4. Students did not do a good job at selecting the number that a model of base-10 blocks represented.
They were not good at making decisions when the piece that represented one whole changed.
In this example, what numbers does this model represent?
53
5.3
represents 1
0.53
0.053
About
1
4
of the students chose 53 as the answer.
5. What decimal represents the shaded part?
0.007
0.07
0.7
7.00
While just over 12 of the students selected the correct answer of 0.07, an equal number(roughly 20%)
each selected the tenths and hundredths.
This could indicate a lack of exposure to this kind of problem.
6. When asked to add two sets of base-10 blocks together, each having large cubes, flats and rods, when
the large cube represented 1, students selected the whole number as the sum.
7. Which number is thirty-seven and 8-hundredths?
37.800
37.08
37.008
37 800
While just over 60% gave the correct answer of 37.08, an equal number answered 37.800 and 37.008.
Recognizing and writing decimal numbers seems to be a problem.
8. 9-0.62
For this question, approximately 20% gave an answer of 53, indicating that they subtracted the 9 from
the 62.
9. Recognizing the correct statement that a base-10 model for subtraction or for division represented was
very poorly done.
10. For a question like
The product of 0.5 x 24.62 is
12.31
24.67
123.1
 students did not recognize the 0.5 as
1
2
and did the calculation when it could have been done mentally.
 chose the 2nd answer indicating they added the numbers with no thought of place value.
 chose the 3rd answer indicating that the 5 was treated as a whole number and multiplied.