Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Which is larger, 0.3 or 0.25? Many students pick 0.25 because 25 looks bigger than 3. Fourth graders learn to compare decimals by reasoning about their size rather than their digits. One reliable way is to compare place by place from the left: 0.3 has 3 tenths and 0.25 has only 2 tenths, so 0.3 is larger. Another is to rename both as hundredths, 0.30 and 0.25, and compare 30 hundredths with 25 hundredths.
Visual models make the reasoning convincing. On a hundred grid, 0.3 fills three whole columns while 0.25 fills only two and a half. On a number line, 0.3 sits to the right of 0.25. As with fractions, the standard reminds students that a comparison is only valid when both decimals refer to the same whole, and it asks them to record results with >, = or < and justify them. Decimals in this standard go to the hundredths place only.
Students think 0.45 > 0.6 because it has more digits. Writing 0.6 as 0.60 shows that 60 hundredths is more than 45 hundredths.
The opposite error appears too: students who learned that tenths are bigger than hundredths decide 0.3 > 0.35. Place by place, both have 3 tenths, and 0.35 has 5 extra hundredths.
When comparing 2.09 and 1.9, students may focus on the decimal digits. The ones place is compared first, and 2 ones beats 1 one.
Order 0.6, 0.45 and 0.06 from least to greatest.
Answer: From least to greatest: 0.06, 0.45, 0.6.
Give students decimal cards and hundred grids and ask them to shade each card before ordering. Pairs designed to trigger both misconceptions, such as 0.5 vs 0.45 and 0.3 vs 0.35, keep the reasoning honest.
Assessment items usually present several statements with >, = or < and ask which are true, or show a number line and ask where a decimal belongs. A quick habit of adding a zero to make equal-length decimals works well for these.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: B) >
0.3 = 0.30 and 30 hundredths is more than 25 hundredths, so 0.3 > 0.25.
Answer: D) 0.6
Compare tenths digits: 4, 6, 0 and 5. The 6 tenths in 0.6 is the most, so 0.6 is greatest.
Answer: =
0.7 is 7 tenths and 0.70 is 70 hundredths. These name the same amount, so they are equal.
Answer: B) 0.09, 0.3, 0.35
As hundredths these are 9, 30 and 35. So the order is 0.09, 0.3, 0.35.
Answer: A) 0.45 has fewer tenths than 0.6
0.45 has 4 tenths and 0.6 has 6 tenths. Renamed as hundredths, 45 < 60, so 0.45 < 0.6.
Answer: 2 (also accepted: 0.02)
12.5 = 12.50. The difference is 12.50 - 12.48 = 0.02 seconds, which is 2 hundredths.
A full lesson with slides, activities and an exit ticket on comparing decimals to hundredths, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 4.NF.C.7 with an answer key, ready in about a minute.
Make a worksheet βTurn comparing decimals to hundredths into a quiz students answer online that marks itself, with a class summary for you.
Build a test βLine up the decimal points and compare digits from left to right. Adding zeros so both decimals have the same number of places, like 0.3 and 0.30, often helps.
No. Fourth graders compare decimals to hundredths. Comparing to thousandths is part of 5.NBT.A.3.