Align decimal points, compare from left to right, and stop at the first unequal place.

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Comparing Decimals Simulation

Place value makes comparison visible

Paused — change the decimals or press Start.

Experiment

Mission: align place values and find the first digit that differs.

Decimals to compare

Decimal A 0.50

Type A

Decimal B 0.500

Type B

Display precision

Simulation speed 1×

Comparison rule

Whole numbers → tenths → hundredths → thousandths. Stop at the first difference.

0.50 = 0.50 because every aligned place is equal.

Difference graph

View and focus

Zoom 1.00×

No object selected.

Teacher tools

Interactive visual lesson

Step 1 of 100%

Ready. Narration will not start automatically.

Language and narrator

Language

Narrator

Narration speed 1×

Narration volume 125%

Embedded narration audio uses clarity filtering, compression and enhanced tab volume, so tab recording can capture clean speech without a microphone.

1. What comparing decimals means

What to watch: The first ten seconds define the topic while the comparison scene builds.

Chapters

Comparing Decimals Simulation

This comparing decimals simulation uses place-value blocks, grids, number lines, money and measurements to make decimal size visible.

Learning objectives

Compare decimals through thousandths using place value.
Explain why trailing zeros do not change a decimal’s value.
Use number lines and area models to verify comparisons.
Apply decimal comparison to money and measurement.

Key concepts and formulas

Align decimal points. Compare from the greatest place value toward the smallest. At the first unequal place, the number with the greater digit is greater.

Equivalent-decimal rule: 0.5 = 0.50 = 0.500.

Difference check: A − B is positive when A > B, zero when A = B, and negative when A < B.

Suggested experiments

Compare 0.9 with 0.81 and explain why digit count is misleading.
Compare 2.05 with 2.5 using the money model.
Compare 0.473 with 0.468 and identify the deciding place.
Set equal values with different trailing zeros.

Questions for exploration

Why is 0.40 equal to 0.4?
Can later digits overturn an earlier unequal digit?
How does zooming a number line reveal hundredths?

Real-world applications

Decimal comparison is used in prices, metric measurements, sports times, scientific data, medicine and engineering tolerances.

Common misconceptions

More decimal digits do not automatically make a number larger.
Decimals must be aligned by decimal point, not by their final digit.
A trailing zero changes notation, not quantity.

Knowledge check

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