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Chapter 2 - You measure tick to tick what about the spaces between?

When they complete the measurements?

Absolutely! Here's a side-by-side comparison table showing the tick marks, their measurements, and the gap sizes for a standard ruler (inch and centimeter sides) and a protractor (degrees):

Ruler (Inch Side) Gap Size Ruler (Centimeter Side) Gap Size Protractor Gap Size

Tick: 0" Tick: 0 cm Tick: 0°

1/16" 1 mm 1°

Tick: 1/16" Tick: 1 mm Tick: 1°

1/16" 1 mm 1°

Tick: 1/8" Tick: 2 mm Tick: 2°

1/16" 1 mm 1°

Tick: 3/16" Tick: 3 mm Tick: 3°

1/16" 1 mm 1°

Tick: 1/4" Tick: 4 mm Tick: 4°

1/16" 1 mm 1°

Tick: 5/16" Tick: 5 mm Tick: 5°

1/16" 1 mm 1°

Tick: 3/8" Tick: 6 mm Tick: 6°

1/16" 1 mm 1°

Tick: 7/16" Tick: 7 mm Tick: 7°

1/16" 1 mm 1°

Tick: 1/2" Tick: 8 mm Tick: 8°

1/16" 1 mm 1°

Tick: 9/16" Tick: 9 mm Tick: 9°

1/16" 1 mm 1°

Tick: 5/8" Tick: 10 mm (1 cm) Tick: 10°

1/16" 1 mm 1°

Tick: 11/16" Tick: 11 mm Tick: 11°

1/16" 1 mm 1°

Tick: 3/4" Tick: 12 mm Tick: 12°

1/16" 1 mm 1°

Tick: 13/16" Tick: 13 mm Tick: 13°

1/16" 1 mm 1°

Tick: 7/8" Tick: 14 mm Tick: 14°

1/16" 1 mm 1°

Tick: 15/16" Tick: 15 mm Tick: 15°

1/16" 1 mm 1°

Tick: 1" Tick: 16 mm Tick: 16°

Key Points

Ruler (Inch Side): Each gap is 1/16", ticks are at 0", 1/16", 1/8", ... up to 1".

Ruler (Centimeter Side): Each gap is 1 mm, ticks are at 0 mm, 1 mm, 2 mm, ... up to 10 mm (1 cm).

Protractor: Each gap is 1°, ticks are at 0°, 1°, 2°, ... up to 180° (or 360° for a full-circle protractor).

This pattern repeats for the full length of the ruler or protractor.

If you want the table extended or customized for a specific range, just let me know!

A standard half-circle protractor (the most common type) only appears to be half a circle, but it's designed to measure angles up to 180° while still allowing you to measure a full 360° through clever design.

How Half-Circle Protractors Work

The key to understanding half-circle protractors is their dual scale system:

Two sets of numbers: A half-circle protractor has two scales - one on the outer edge and one on the inner edge

Outer scale: Runs from 0° to 180° from left to right

Inner scale: Runs from 180° to 0° (or sometimes labeled as 0° to 180° right to left)

This dual-scale design allows you to measure angles regardless of which direction they open:

You always place the center of the protractor on the vertex of the angle

You align the 0° mark with one ray of the angle

Then you read the measurement where the other ray crosses the appropriate scale

Why This Works for Full Circles

Even though the protractor only shows 180°, you can measure any angle up to 360° by:

For angles 0°-180°: Measure directly using the appropriate scale

For angles 180°-360°: Use the "circle trick" - subtract the angle from 360° and measure the complementary angle instead

For example, to draw a 335° angle:

You can't measure 335° directly on a half-circle protractor

So you calculate: 360° - 335° = 25°

You draw a 25° angle and label the exterior angle as 335°

Full-Circle vs. Half-Circle Protractors

While full-circle protractors do exist and can measure angles up to 360° directly, half-circle protractors are more common in schools and basic geometry because:

They're more compact and easier to handle

Most angles encountered in basic geometry are less than 180°

They're still capable of measuring or constructing any angle with the right technique

The half-circle design is essentially a space-efficient way to provide full functionality while being more portable and practical for everyday use.

Here's a vertical list for a standard 180° protractor, labeling each tick and the gaps (spaces) between them, just like you'd see on the tool:

Protractor Tick and Gap List (0° to 180°)

text

Tick: 0°

Gap: (1° space)

Tick: 1°

Gap: (1° space)

Tick: 2°

Gap: (1° space)

Tick: 3°

Gap: (1° space)

Tick: 4°

...

Tick: 89°

Gap: (1° space)

Tick: 90° (center/top of semicircle)

Gap: (1° space)

Tick: 91°

...

Tick: 179°

Gap: (1° space)

Tick: 180°

Each tick marks a degree (every 1°).

Each gap is the space between two ticks (1° apart).

No gap before 0° or after 180°-the protractor starts and ends with a tick at the edge.

This pattern repeats for all degrees on the protractor. If you're using a 360° protractor, just continue the same pattern up to 360°.

Great question! Let's clarify:

Are There Gaps at the Beginning and End?

No, there is not a gap before the very first tick (0) or after the last tick (1 inch or 1 cm) on a standard ruler.

The first tick (at 0) is the starting edge of the ruler, and the last tick (at 1 inch/1 cm, or at the end of the ruler) is the ending edge.

Gaps only exist between tick marks-you measure the space from one tick to the next, but not before the first or after the last.

Visual Example (Inch Side, 0" to 1")

text

[Edge] Tick: 0"

Gap: (1/16" space)

Tick: 1/16"

Gap: (1/16" space)

...

Tick: 15/16"

Gap: (1/16" space)

Tick: 1" [Edge]

The first tick (0") is right at the edge-no gap before it.

The last tick (1") is at the other edge-no gap after it.

All gaps are between ticks.

Visual Example (Centimeter Side, 0 cm to 1 cm)

text

[Edge] Tick: 0 cm

Gap: (1 mm space)

Tick: 1 mm

Gap: (1 mm space)

...

Tick: 9 mm

Gap: (1 mm space)

Tick: 1 cm [Edge]

Summary Table

Position Tick? Gap?

Start of ruler Yes No

Between ticks Yes Yes

End of ruler Yes No

In short:

The ruler starts and ends with a tick (no gap before or after).

Gaps are only between ticks.

If you want a diagram or further explanation, just ask!

Absolutely! Here's a vertical list for both the inch and centimeter sides, clearly identifying tick marks and the gaps (spaces) between them, just like you'd label a ruler.

Inch Side (Imperial, 0" to 1")

text

Tick: 0"

Gap: (1/16" space)

Tick: 1/16"

Gap: (1/16" space)

Tick: 1/8"

Gap: (1/16" space)

Tick: 3/16"

Gap: (1/16" space)

Tick: 1/4"

Gap: (1/16" space)

Tick: 5/16"

Gap: (1/16" space)

Tick: 3/8"

Gap: (1/16" space)

Tick: 7/16"

Gap: (1/16" space)

Tick: 1/2"

Gap: (1/16" space)

Tick: 9/16"

Gap: (1/16" space)

Tick: 5/8"

Gap: (1/16" space)

Tick: 11/16"

Gap: (1/16" space)

Tick: 3/4"

Gap: (1/16" space)

Tick: 13/16"

Gap: (1/16" space)

Tick: 7/8"

Gap: (1/16" space)

Tick: 15/16"

Gap: (1/16" space)

Tick: 1"

Centimeter Side (Metric, 0 cm to 1 cm)

text

Tick: 0 cm

Gap: (1 mm space)

Tick: 1 mm

Gap: (1 mm space)

Tick: 2 mm

Gap: (1 mm space)

Tick: 3 mm

Gap: (1 mm space)

Tick: 4 mm

Gap: (1 mm space)

Tick: 5 mm

Gap: (1 mm space)

Tick: 6 mm

Gap: (1 mm space)

Tick: 7 mm

Gap: (1 mm space)

Tick: 8 mm

Gap: (1 mm space)

Tick: 9 mm

Gap: (1 mm space)

Tick: 1 cm

How to Read This

Tick: The line or mark you see on the ruler (where you'd read the measurement).

Gap: The space between two tick marks (always the same size: 1/16" on the inch side, 1 mm on the metric side).

This pattern repeats for every inch and centimeter along the entire ruler.

If you want a longer list (e.g., for 2 inches or 5 cm), just let me know!

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