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Math · Grade 5 Math

Chapter 1: Place Value and Decimals

Comparing Decimals to Thousandths

Biggest place first, every time.

Lesson
4
Time
About 15 minutes
0 of 8 done

Step 1: Let's Learn

Read it, or press Listen and follow the words.

Start at the biggest place. The first place where the digits differ decides everything.

Match the places first

Compare 0.4 and 0.386 by writing 0.400. Then 4 against 3 settles it.

Length still does not decide

0.9 beats 0.1234, even though the second has far more digits.

Compare place by place from the left

For 0.472 against 0.48, look at tenths: 4 and 4, equal. Hundredths: 7 against 8. Eight hundredths beats seven, so 0.48 is larger. The first difference from the left settles it, and nothing to the right can overturn it.

Padding makes it obvious

Write 0.48 as 0.480 and compare 472 thousandths with 480 thousandths. Padding with zeros puts both numbers in the same unit, which is the same move as finding a common denominator. It costs nothing and removes all doubt.

More digits is still not bigger

0.472 has three digits and 0.48 has two, yet 0.48 is larger. The whole-number instinct that longer means bigger fails completely for decimals. If you catch yourself reaching for it, pad and compare as counts instead.

Ordering a list

Pad every number to the same number of decimal places first, then order them as if they were whole numbers. Doing the padding for all of them up front is far more reliable than comparing pairs one at a time and hoping the order is consistent.

Step 2: Try It Yourself

Tap and try it out.

Two decimals on one line. Whichever sits further right is bigger.

40/100 = 0.40 = 0.4

38/100 = 0.38

0.00.10.20.30.40.50.60.70.80.91.0

0.4 covers more squares than 0.38, so it is greater.

Step 3: Watch an Example

One step at a time.

Watch Leo Order Three Decimals

Leo orders 0.7, 0.68, and 0.702.

  1. Step 1

    He writes them all to three places: 0.700, 0.680, 0.702.

Step 4: Your Turn

Practice makes it stick.

The Times

Problem 1 of 2

Which is faster, a time of 9.85 seconds or 9.9 seconds?

The Weights

Problem 2 of 2

Which is heavier, 2.305 kg or 2.35 kg?

Which Is Bigger?

1 of 4

Which is bigger, 0.5 or 0.462?

2 of 4

Which is bigger, 0.207 or 0.27?

3 of 4

Which is bigger, 0.9 or 0.1234?

4 of 4

Which place do you compare first?

Step 5: Quick Check

Show what you know.

Question 1 of 2

Which is bigger, 0.608 or 0.61?

Question 2 of 2

Does a decimal with more digits have to be bigger?

What You Learned

  • Write both decimals to the same number of places.
  • Compare from the biggest place, moving right.
  • The first place where they differ decides.