How does the tool identify repeating decimals?

It tracks remainders during digit-by-digit long division; when a remainder repeats, the sequence of quotient digits is flagged as the exact repetend.

What conditions make a fraction a terminating decimal?

A fraction terminates in decimal form if its fully reduced denominator contains only the prime factors 2 and 5.

Which visual models are linked to the input values?

The visualizer displays a pie chart, a fraction bar, a 10×10 percent grid, and a 0–1 number line, all updating in real time.

Can I interactively change values without retyping numbers?

Yes, an integrated per-mille interactive slider allows continuous value adjustments that synchronize all visual models and readouts.

What types of practice exercises are provided?

The tool includes deterministic exercises covering fraction simplification, repetend detection, and comparisons between percentages and decimals.

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Fraction / Decimal / Percent Visual Tutor

One value, three linked notations — pie, bar, percent grid and number line — with a live-synced slider, exact repetend detection and practice exercises.

Details

What this tool helps you do

Implements long-division expansion with remainder tracking (a repeated remainder starts the repetend; length ≤ denominator − 1), the terminating test (reduced denominator has only prime factors 2 and 5), and GCD simplification. The playground runs as a sandboxed data-URI iframe (allow-scripts, no network); the per-mille slider drives pie, bar, grid, number line and all three readouts simultaneously. Exercises are deterministic: simplification, repetend spotting, percent-vs-decimal comparison.

Execution

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Prepared example runs

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2 examples

Three quarters as the anchor example

3/4 shown at once as a 75%-filled pie, a three-of-four bar, 75 blue grid squares and a marker at 0.75 — with the terminating-decimal explanation and the three practice cards.

<section class="fdp">3/4 ⇄ 0.75 ⇄ 75% · pie + bar + 100-grid + number line · playground slider · 3 exercises</section>

One third — spot the repeating decimal

1/3 never terminates: the tutor detects the repetend “3” (overline notation), shows ≈ 33.3%, and the repetend exercise asks about the fraction itself.

<section class="fdp">1/3 ⇄ 0.3̅ ⇄ ≈ 33.3% · repetend detected: “3” · repeating-decimal exercise</section>

Inputs

Set the required fields, then run the tool.

6 options

SettingsAdjust formats, ranges, numbers, and modes.5

Input formselectOptionalNumeratornumberOptionalDenominatornumberOptionalDecimal value (0–1)numberOptionalPercent value (0–100)numberOptional

TogglesEnable or disable optional behavior.1

Show practice exercisescheckboxOptionalEnabled when checked

Result

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Samples

Fraction / Decimal / Percent Visual Tutor

What this tool helps you do

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Prepared example runs

Inputs

Result

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Key facts

Overview

When to use

How it works

Use cases

Examples

1. Visualizing Common Terminating Fractions

2. Detecting Repeating Decimal Periods

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