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Math Foundations

You will compare and order decimals by representing them on a grid, locating them on a number line, or using place value.

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After completing this tutorial, you will be able to complete the following:

- Use place value to represent decimals (tenths and hundredths) in pictorial representations.
- Use a number line to order decimals.
- Use place value to compare and order decimals (through thousandths) by lining up the decimals.

The decimals are numbers having one or more digits to the right of a decimal point.

Example: 1.23

A decimal fraction is a fraction whose denominator (the bottom number) is a number such as 10, 100, 1000, etc (in other words, a power of ten). A digit in a decimal number has a value based on its place. The places to the left of the decimal point are whole numbers and can be ones, tens, hundreds, etc. The places to the right of the decimal represent rational numbers or fractional parts of a whole number and can be tenths, hundredths, etc. This table shows the decimal place value for various positions:

Place (underlined) Name of Position

1.234567 Ones (units) position

1.234567 Tenths

1.234567 Hundredths

1.234567 Thousandths

1.234567 Ten thousandths

1.234567 Hundred Thousandths

1.234567 Millionths

Note that adding extra zeros to the right of the last decimal digit does not change the value of the decimal number.

Remember, the whole number portion of a decimal number is represented by the digits to the left of the decimal place. As we move further left, every number place gets 10 times bigger. As we move further right, every number place gets 10 times smaller (one tenth as large). The word "decimal" means "based on ten".

Visual representations can be used to represent decimal numbers.

The chart below illustrates how decimal numbers are represented using visual representations. In this Activity Object, whole number representations are given, and only the decimal numbers need to be visually represented.

Each long bar in the visual representation represents one tenth. To represent a decimal such as 0.4 - four tenths, shade in four long bars.

Each square represents one hundredth. To represent a decimal such as 0.04 - four hundredths, shade in four squares.

When comparing decimals, you need to look at the first place where the digits differ.

Begin by lining up the decimal points. If needed, add a zero or zeros to the right of the number so that each has the same number of decimal places. Starting at the left, find the first place the digits differ, than compare the digits.

Approximate Time | 20 Minutes |

Pre-requisite Concepts | Students should be familiar with the concept of decimals and place value. |

Course | Math Foundations |

Type of Tutorial | Concept Development |

Key Vocabulary | compare decimals, decimals, order decimals |