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## Understanding Decimals

#### Introduction

The decimal system is used to express numbers that are not whole numbers. Any number can be written in decimal notation, and decimals can be added, subtracted, multiplied, and divided just like any other number.

#### Terms

Decimal Point - The decimal point looks like a period and is always placed after the “ones” position of a number.
Decimal Notation - Decimal notation is useful for writing numbers which are not whole numbers.
Whole Number - A whole number is a number with nothing but zeroes after the decimal point.

## Lesson

Any real number can be written as a decimal. The whole number 3 for example, can be written as

$3=3.0=3.00=3.000$, etc.,

#### Decimal Place Value Chart

Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones
Decimal Point
Tenths
Hundredths
Thousandths
Ten-thousandths
Hundred Thousandths
Millionths
3.
3.
3.
3.

although the trailing zeroes are usually ignored. Anything other than zero after the decimal point means that the number is not whole. 3.52, for example, is a number between 3 and 4. The first space after the decimal is referred to as the “tenths” place, the next space is known as the “hundreths” place, the third space is the “thousandths” place, etc.

Note: Just like it is acceptable to add zeroes at the end of decimals (0.5 can be written as 0.50 or 0.500) it is also acceptable to omit zeroes as long as they are after the decimal point and not followed by further numbers (1.30 can be written as 1.3).

## Examples

There are 10 total boxes in the grid
6 of the boxes are shaded
6 out of 10 can be written as the decimal 0.6 (six Tenths)
There are 100 total boxes in the grid
64 of the boxes are shaded
64 out of 100 can be written as the decimal 0.64 (sixty four Hundredths)