Long Hundred to Gross conversion

How to convert long hundred to gross?

Sure, let's break down how to convert from Long Hundred to Gross, and also look at real-world examples for other quantities.

Conversion from Long Hundred to Gross

1. Definition of Long Hundred: A Long Hundred (also known as a "great hundred") is equal to 120 units.

2. Definition of Gross: A Gross is equal to 144 units.

To convert 1 Long Hundred to Gross, you need to express 120 units in terms of Gross (144 units): $1 \text{ Long Hundred} = 120 \text{ units}$

To find this in Gross: $\frac{120 \text{ units}}{144 \text{ units per Gross}} = \frac{120}{144} = \frac{5}{6}$

So, 1 Long Hundred is equal to $\frac{5}{6}$ (or approximately 0.8333) of a Gross.

Real-World Examples

Let's consider other quantities of Long Hundreds and how they can be applied:

2 Long Hundreds:

$2 \text{ Long Hundreds} = 2 \times 120 = 240 \text{ units}$

In terms of Gross: $\frac{240 \text{ units}}{144 \text{ units per Gross}} = \frac{240}{144} = \frac{5}{3}$

So, 2 Long Hundreds equal $\frac{5}{3}$ Gross (or about 1.6667 Gross).

3 Long Hundreds:

$3 \text{ Long Hundreds} = 3 \times 120 = 360 \text{ units}$

In terms of Gross: $\frac{360 \text{ units}}{144 \text{ units per Gross}} = \frac{360}{144} = \frac{5}{2}$

So, 3 Long Hundreds equal 2.5 Gross.

Real World Examples

1. Egg Cartons: If you are a farmer with 1 Long Hundred of eggs:

   • You have 120 eggs.
   • In terms of dozens (a common measure for eggs), you have $\frac{120}{12} = 10$ dozen eggs.
   • In terms of Gross, you have $\frac{120}{144} = \frac{5}{6}$ Gross of eggs.

2. Pencil Boxes: Suppose your factory packs pencils in boxes of 12:

   • If you have an order for 1 Long Hundred of boxes, that's 120 boxes.
   • Since each box contains 12 pencils, you multiply to get the total number of pencils: $120 \times 12 = 1440 \text{ pencils}$.
   • For larger scale orders measured by the Gross (144 units), you see you have exactly 10 Gross of pencils ($\frac{1440}{144} = 10$).

3. Screws in Construction: If a carpenter needs 2 Long Hundreds of screws:

   • They need 240 screws.
   • Checking inventory for screws in packets of 144, this is equivalent to 1 and $\frac{2}{3}$ packets, or 1.66 packets of screws.

The concept of Long Hundred and Gross can come in handy, especially in fields dealing with bulk quantities, providing a convenient intermediate measure between dozens and larger groupings.