Small Gross (sm-gr) to Long Hundred (long-hundred) conversion

Small Gross to Long Hundred conversion table

Small Gross (sm-gr)Long Hundred (long-hundred)
00
11
22
33
44
55
66
77
88
99
1010
2020
3030
4040
5050
6060
7070
8080
9090
100100
10001000

How to convert small gross to long hundred?

Small Gross and Long Hundred are both archaic units of quantity. Understanding their relationship is key to converting between them.

Understanding the Units

Before we dive into the conversion, let's clarify what these units represent:

  • Small Gross: A small gross is equal to 12 dozens, or 144 items.
  • Long Hundred: A long hundred, also known as a great hundred, is equal to 120 items.

Converting Small Gross to Long Hundred

To convert from Small Gross to Long Hundred, we need to determine how many Long Hundreds are equivalent to one Small Gross.

Step-by-step Conversion:

  1. Start with the definition: 1 Small Gross = 144 items

  2. Determine the ratio: We want to find out how many Long Hundreds are in 144 items. Since 1 Long Hundred = 120 items, we can set up the following ratio:

    144 items120 items/Long Hundred\frac{144 \text{ items}}{120 \text{ items/Long Hundred}}

  3. Calculate: Divide 144 by 120.

    144120=1.2\frac{144}{120} = 1.2

  4. Result: 1 Small Gross = 1.2 Long Hundreds

    This means that one small gross contains 1.2 long hundreds.

    1 Small Gross=1.2 Long Hundreds1 \text{ Small Gross} = 1.2 \text{ Long Hundreds}

Converting Long Hundred to Small Gross

To convert from Long Hundred to Small Gross, we perform the inverse operation.

Step-by-step Conversion:

  1. Start with the definition: 1 Long Hundred = 120 items

  2. Determine the inverse ratio: We want to find out how many Small Grosses are in 120 items. Since 1 Small Gross = 144 items, we set up the following ratio:

    120 items144 items/Small Gross\frac{120 \text{ items}}{144 \text{ items/Small Gross}}

  3. Calculate: Divide 120 by 144.

    120144=0.8333...56\frac{120}{144} = 0.8333... \approx \frac{5}{6}

  4. Result: 1 Long Hundred = 56\frac{5}{6} Small Grosses. Or approximately 0.833 Small Gross.

    This means that one long hundred contains approximately 0.833 of a small gross.

    1 Long Hundred=56 Small Gross1 \text{ Long Hundred} = \frac{5}{6} \text{ Small Gross}

Base 10 vs Base 2

The conversion between Small Gross and Long Hundred remains the same whether you're using base 10 (decimal) or base 2 (binary) systems. These units are based on counts of items, and the mathematical relationship between them doesn't change with different numerical bases.

Real-World Examples

While Small Gross and Long Hundred are not commonly used in modern commerce, the concept of converting between different units of quantity is still relevant. Here are some related examples:

  1. Dozens and Individual Items:
    • If you have 3 dozens of eggs, you can convert this to individual eggs by multiplying by 12 (since 1 dozen = 12 items).
    • 3 dozens = 3×12=363 \times 12 = 36 eggs
  2. Reams and Sheets of Paper:
    • A ream of paper typically contains 500 sheets. If you need to determine how many reams are needed for 2000 sheets, you would divide 2000 by 500.
    • 2000 sheets=2000500=4 reams2000 \text{ sheets} = \frac{2000}{500} = 4 \text{ reams}
  3. Units of Currency:
    • Converting between dollars and cents involves understanding that 1 dollar = 100 cents.
    • $5 = 5×100=5005 \times 100 = 500 cents

These examples highlight how conversion between units of quantity is a fundamental concept used across various scenarios.

Historical Note

The terms "small gross" and "long hundred" are remnants of older systems of counting and commerce. While they may not be in widespread use today, understanding these historical units provides insight into the evolution of measurement systems.

See below section for step by step unit conversion with formulas and explanations. Please refer to the table below for a list of all the Long Hundred to other unit conversions.

What is a Small Gross?

A small gross, also known as a short gross, is a unit of quantity equal to 12 dozens, or 144 items. It's primarily used for counting items sold in bulk. It's related to a gross, which is equal to 12 dozens or 144 items but it is a historical term less commonly used nowadays.

Formation of Small Gross

The term "gross" originates from the Old French word "grosse," meaning "large" or "thick." Its adoption as a counting unit likely stems from the convenience of representing a quantity larger than a dozen but still manageable for commerce. The "small" modifier is used to distinguish it from other similar terms that are now obsolete.

  • Dozen: 12 items
  • Small Gross: 12 dozens = 144 items
  • Gross: 12 dozens = 144 items

Historical Context and Usage

While there isn't a specific law or famous figure directly tied to the small gross, its significance lies in its historical use in trade and inventory management. Before the widespread adoption of decimal-based systems, units like the small gross provided a standardized way to handle bulk quantities. Today, it's more common to directly use the number 144 or simply refer to a "gross" because "small gross" became an outdated and redundant term.

Real-World Examples of Quantities Measured in Gross or Multiples Thereof

Although using "small gross" is outdated, thinking in terms of 144 (or dozens of dozens) can be helpful:

  • Screws/Nails/Fasteners: In manufacturing or hardware, a large quantity of small components like screws, nails, or fasteners may be purchased, stored, or inventoried in multiples of gross to simplify handling and record-keeping.
  • Buttons/Beads/Craft Supplies: Craft suppliers or manufacturers might sell small items like buttons or beads in gross quantities.
  • Office Supplies: Items like pencils, pens, erasers, or paper clips might be purchased by businesses in gross quantities for stocking supply rooms.
  • Packaging: A company needing to package a large order might calculate the amount of packaging that they need in units of Gross. For example, they might need 2 gross of boxes or bubble wraps to fulfill an incoming order.

What is long hundred?

The long hundred, also known as a great hundred or a twelve-score, is an obsolete unit of quantity equal to 120 items. It's a relic of a counting system where calculations were sometimes done in base-12 or base-20, rather than the standard base-10 system we use today.

Origin and Formation

The long hundred arises from the practice of counting in dozens (groups of 12). Unlike the "short hundred" (decimal hundred) that contains 100 items, the long hundred is based on a duodecimal system influence or simply a traditional way of counting specific goods. It is formed by multiplying twelve (a dozen) by ten, resulting in 120.

  • Dozen: 12 items
  • Long Hundred: 12 dozens, or 12 * 10 = 120 items

This contrasts with the decimal system, where a hundred is simply 10 * 10 = 100.

Historical Context and Usage

The long hundred was most commonly used in trade and commerce, particularly when dealing with goods that were easily grouped into dozens, such as eggs, nails, or other small wares. It provided a convenient way to count and package these items. While no specific laws directly mandated its use, it was a customary practice deeply ingrained in certain industries.

Examples of Quantities Using Long Hundred

Here are a few examples of how long hundreds might be used:

  • Nails: A hardware store might sell nails in long hundreds, making it easier to manage inventory.
  • Herrings: In the herring trade, fish were often counted and sold using the long hundred.
  • Other small wares: Any items that were easy to bundle into dozens could be sold using this unit.

Let's say you are buying nails, then

1 Long Hundred = 120 nails.

So buying 3 long hundreds would get you 360 nails.

3×120=3603 \times 120 = 360

Why did long hundreds cease to exist?

The adoption of the metric system and decimal-based accounting practices gradually led to the decline and eventual obsolescence of the long hundred. These modern systems provided greater efficiency and standardization.

Complete Small Gross conversion table

Enter # of Small Gross
Convert 1 sm-gr to other unitsResult
Small Gross to Pieces (sm-gr to pcs)120
Small Gross to Bakers Dozen (sm-gr to bk-doz)9.2307692307692
Small Gross to Couples (sm-gr to cp)60
Small Gross to Dozen Dozen (sm-gr to doz-doz)0.8333333333333
Small Gross to Dozens (sm-gr to doz)10
Small Gross to Great Gross (sm-gr to gr-gr)0.06944444444444
Small Gross to Gross (sm-gr to gros)0.8333333333333
Small Gross to Half Dozen (sm-gr to half-dozen)20
Small Gross to Long Hundred (sm-gr to long-hundred)1
Small Gross to Reams (sm-gr to ream)0.24
Small Gross to Scores (sm-gr to scores)6
Small Gross to Trio (sm-gr to trio)40