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Compare Decimals to Thousandths Using >, =, and <

Students compare two decimals to the thousandths place by analyzing the value of digits in each place, starting from the largest place. They record comparisons using the symbols >, =, and < and justify their reasoning using place value understanding.

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Compare Decimals to Thousandths Using >, =, and <

Grade 5 · Reading, Writing, and Comparing Decimals to Thousandths · question 1 of 3

0 of 20

20 rungs. A star at the top.

Which of these makes 0.200 = blank true: 0.198, 0.199, 0.2 or 0.201?

How it is taught

0:00 of 5:28

Decimals are compared place by place from the left.

The first place that differs decides which is greater.

Read it: Comparing decimals

0.452 and 0.46 on the place chart, ones over ones. The ones match, and the tenths match: 4 and 4. The hundredths decide: 5 hundredths against 6. So 0.452 < 0.46.

  1. Write both numbers on the place chart, ones over ones, and write in a 0 where one is shorter.
  2. Compare the digits from the left, one place at a time.
  3. The first place where the digits differ decides: the bigger digit makes the bigger number.

Each place is worth ten of the place to its right, so the first difference outweighs every place after it.

0.46 is 0.460: writing in a 0 does not change a decimal.

More digits do not make a decimal bigger: 0.452 has more digits than 0.46, and 0.452 is less.

Line up the places and compare from the left; the first place that differs decides.

Calling 0.452 bigger because it has more digits.

Compare by place: in the hundredths, 5 is less than 6, so 0.452 < 0.46.

0.374 ___ 0.38 — <. The tenths match; in the hundredths, 7 is less than 8: 0.374 < 0.38.

0.345 vs 0.354

Let's compare two decimals: zero point three four five, and zero point three five four. Which one is bigger?

Compare 0.345 and 0.354Which decimal is greater?onestenthshundredthsthousandths0.3450.35540 = 0 — equal, keep going3 = 3 — still tied4 vs 5 — which is bigger?4 < 5 — the second number wins!0.345 < 0.354ANSWER<0.345 < 0.354
Grade 5 · Compare place by place using >, =, <

First, we line them up by place value so we can compare digit by digit, starting from the left.

Start with the ones place. Both numbers have zero — they are equal here, so we keep going.

Now the tenths. Both are three — still tied. Move to the next place.

Now look at the hundredths place. What do we see?

Four versus five. Five is bigger! Once we find a difference, we can stop — we do not even need the thousandths.

So zero point three four five is less than zero point three five four. We write it using the less-than sign.

Always compare from left to right, place by place. The first place that is different decides the answer. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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