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Hundred chart dog bone

The hundred chart dog bone is a type of dog bone used in English and some other traditional counting systems. It is also the name of a related number line layout, the Hundred Chart.

It is named for its resemblance to the shape of a dog's head. The chart's 100 divisions are divided into ten "paws" (the first five divisions, corresponding to the ears, resemble toes, and the last five, the head, resemble the other four feet). The ten "paws" are also sometimes referred to as "ears".

Chart variants

The following charts are described in the Wikipedia entry for a hundred chart:

The hundred chart is a number line for whole numbers, which uses one set of numbers for whole numbers up to 10 (and the rest for multiples of 10) and a separate set of numbers for multiples of 100, including multiples of 10 from 5 upwards. The hundred chart is also used as the basis for the hundred chart variant, which is used for counting by 10s and 100s in the form "one of each" to indicate a multiple of 10.

The hundred chart for whole numbers (and in fact any number line) can be thought of as a special case of the hundred chart variant: in this chart, the whole number line is replaced with a whole number multiple of 100.

This chart is also used in some other English-speaking countries, especially in Australia.

It is also known as a "chart of the four" because it can be considered the smallest of the four charts of the four.

Another variant is the chart of the five (or "chart of five"), which is a number line where all the numbers are five digits long.

It can be represented visually as follows:

100 × 10^n = 10

100 × 10^n − 100 = 10

So the ten digits of a number (up to 100,000) are each written to the 10 "paws" of the chart.

The hundred chart is most often found in the form used to teach arithmetic, which consists of a table with each number labelled with the appropriate ten digits. However, a more traditional form of the hundred chart is shown at the left.

A variant called the "hundred chart variant" (or "chart of ten") is used in some English-speaking countries, especially in Australia, in arithmetic lessons.

It is usually called a "hundred chart" because each number in the chart is written with its ten digits, not the number of digits in the number itself, e.g. in the chart shown, the number 10,200 is shown as "one hundred and two hundreds". It is named after its resemblance to a chart of 10.

The "hundred chart variant" is a hundred chart where all numbers are multiples of 100, but each number is written as ten digits. For example, the number 1,000,000 in the chart is written as "one million".

This variant of the hundred chart can also be shown as follows:

The "hundred chart variant" of the hundred chart, being based on 10 and 100, is the smallest of the four charts of the four, which means that it contns the fewest numbers. It is sometimes also called a "chart of the five" because it contns numbers all five digits long, the smallest number being 5,000,000.

This chart can be represented visually as follows:

100 × 10^n − 100 = 10

In other systems

In the numbering systems of other languages, the number 100 is expressed differently. For example, in Russian the hundred is not divided into 10 "ears" or "paws", instead, there are 11 fingers. Each of these digits counts 10 times:

1 – 10

2 – 20

3 – 30

4 – 40

5 – 50

6 – 60

7 – 70

8 – 80

9 – 90

0 – 100

Similarly, in the Arabic numbering system, the 100th is the last digit (the zero), and the number is divided into ten "fingers" (sometimes called "toes" or "paws", with fingers 0–9).

The Russian numbering system is sometimes called the "Russian hundred" and the Arabic numbering system is sometimes called the "Arabic hundred".

It is sometimes clmed that the Russian numbering system has evolved over time.

The Spanish numbering system has only six digits:

100 is the last digit (zero)

1 to 9 are the ten "fingers" (sometimes called "toes")

In a variant of this numbering system, the second and third digits have been reversed, so the digits 1–9 are all written with their "toes" on the left.

In other countries

Ireland

In Ireland, the numbers up to 1000 are given on the "100 chart". This is also used for any number written as a string of tens and ones: it's like the hundred chart with the number 100 on it. So numbers like 1010 and 1110 are also written as 100. A further complication arises because the 100 chart does not have any numbers written in the 1000s. Instead, there are separate charts for the numbers up to 100,000 and for numbers in the 10,000s. For example, the number 101,000 would be written as "one hundred, one thousand, zero hundred".

The 100 chart has been in use in Ireland since the 18th century, and is the mn basis for Irish counting in all situations. It is rarely used in Irish numeracy exercises and arithmetic lessons,