The decimal system
As well as human beings naturally having ten fingers for counting, the decimal system has special properties
that make it the easiest 'base' to use for maths. The columns we use are based on
powers of ten:
| 1 | one |
| 10 | ten |
| 100 | hundred |
| 1,000 | thousand |
| 10,000 | ten thousand |
| 100,000 | one hundred thousand |
| 1,000,000 | one million |
| 10,000,000 | ten million |
Note digits are grouped in threes, separated by commas. However!
The idea of commas as power-separators and a dot as a decimal point is more or less unique to
English-speaking countries. In France, Germany, and most of the rest of the world, it is
the other way around! As such, be careful with non-English websites, books or research papers,
As they will be using this different system. For example, 3,456.123 in English would be written 3.456,123 in French,
which is a totally different number in English!
These issues are actually continually discussed in international standards bodies. A recent recommendation
has been to separate groups of three digits with a space, instead of a comma, so for example:
4 567 234 instead of 4,567,234. This website however uses the UK and USA system.
|
As such, when we write something like
3,456 this actually means:
3000 + 400 + 50 + 6
Writing numbers in English
The actual 'rules' are complicated to state, specifically with the use of commas, hyphens and the word 'and.'
The main rule is that that main names for powers are
grouped in threes. As such, English does not have a word for 'ten thousand'
or 'one hundred thousand.'
As such, the written and spoken form uses the following words:
| 1,000 | thousand |
| 1,000,000 | million |
| 1,000,000,000 | billion |
| 1,000,000,000,000 | trillion |
| 1,000,000,000,000,000 | quadrillion |
The last one is very seldom used.
With all that said, it's probably more natural to just learn by example. Have a glance over the list below:
| 56 | fifty-six |
| 100 | one hundred |
| 105 | one hundred and five |
| 456 | four-hundred and fifty-six |
| 1000 | one thousand |
| 1007 | one thousand and seven |
| 1034 | one thousand and thirty-four |
| 3,456 | three thousand, four-hundred and fifty-six |
| 45,000 | forty-five thousand |
| 167,004 | one hundred and sixty-seven thousand and four |
| 307,034 | three-hundred and seven thousand and thirty-four |
| 1,000,003 | one million and three |
| 1,000,453 | one million, four-hundred and fifty-three |
| 1,034,000 | one million and thirty-four thousand |
| 4,323,803 | four million, three-hundred and twenty-three thousand, eight-hundred and three |
This option shows two question types randomly for practice. It will either say something like:
"What is the number 32,247 written in English?" or
"What is the decimal value of the 7 shown in red? 2,567
Difficulty Levels - typical questions :
1:
What is the number 7,578 written in English?
What is the decimal value of the 2 shown in red? 1,442
2:
What is the number 55,715,526 written in English?
What is the decimal value of the 8 shown in red? 858,818,673
3:
What is the number 61,378,953,631,602 written in English?
What is the decimal value of the 7 shown in red? 78,976,794,392,676