Comparing decimals to thousandths
In 5th grade, children learn to compare two decimals to thousandths by the value of each digit, and to record the result with >, =, or <.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 5th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
Which number is greater than 1.5?
- 1.500
- 1.52
- 1.499
Why this matters
Knowing which of two decimals is bigger gives your child a real feel for numbers with a decimal point. Comparing is how you pick the cheaper box, the faster lap, or the heavier bag of apples. It is the base for rounding decimals later this year, and for ordering positive and negative numbers in 6th grade.
If the place names still feel new, your child can review reading and writing decimals to thousandths before comparing two numbers.
Where kids can get stuck
- Thinking the decimal with more digits is larger, so 0.125 seems greater than 0.5 because 125 is greater than 5.
- Deciding the shorter decimal is always larger, so 0.3 seems greater than 0.35 because tenths are bigger than hundredths.
- Missing that zeros at the end change nothing, so they say 0.4 and 0.400 are different instead of equal.
How you can help
- Time short races down the hallway with a phone stopwatch that shows hundredths. Write the times down and have your child put them in order from fastest to slowest, explaining each choice.
- Compare package weights at the grocery store, such as 0.75 pounds and 0.8 pounds of cheese. Ask which is heavier, and have your child explain it using tenths and hundredths.
- Play a quick dice game at the table. Each of you rolls three dice and makes a decimal like 0.536, and the larger number wins the round. The winner says why their number is bigger.
Want a little more? Try Bobby's Math Club for free practice that adapts to your child.
Questions parents ask
Why is my child learning to compare decimals digit by digit?
Because it works every time. Your child lines up the decimal points and starts at the left. The first place where the digits differ decides it. In 0.528 and 0.53, the tenths match, and 3 hundredths beats 2 hundredths, so 0.53 is greater. It is the same habit they already have with whole numbers, carried past the decimal point.
Why does my child think 0.125 is bigger than 0.5?
With whole numbers, more digits really does mean a bigger number, so children carry that habit into decimals. It is a very common stage. Pictures of tenths and hundredths, money, and measuring help your child see that 0.5 covers half of a whole, while 0.125 covers only an eighth of it. Half a dollar against about twelve cents makes the point quickly.
What if my child reads decimals well but mixes up which is bigger?
That's common. Reading and comparing use the same place names, but comparing asks your child to weigh one digit against another. Try writing the two numbers one above the other with the decimal points lined up. Then add zeros so both have three digits after the point, such as 0.700 and 0.689. Now it is 700 thousandths against 689 thousandths.
Make learning math fun
Bobby's Math Club turns 5th grade math practice into something fun to do together.
- Unlimited practice, completely free
- Questions matched to your child’s level, a few minutes a day
- Hints when they are stuck, and a celebration when it clicks
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 5.NBT.A.3: “Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.” Learn how Bobby's Math Club can help your students grow. (Common Core 5.NBT.3)