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Decimal Numbers

What Are Decimals?


In our number system, the position of a digit tells us its value. Let's look at the number 235.
\(235=\)
It is made of three parts:
  • The 5 is in the Ones place, meaning 5 ones (\(5\)).
  • The 3 is in the Tens place, meaning 3 tens (\(30\)).
  • The 2 is in the Hundreds place, meaning 2 hundreds (\(200\)).
Our number system follows a pattern based on 10.
  • When we move left \(\leftarrow\), each place is 10 times bigger. (10 ones make a ten, 10 tens make a hundred).
  • When we move right \(\rightarrow\), each place is 10 times smaller. (A hundred divided by 10 is a ten, a ten divided by 10 is a one).
What happens if we keep moving right? What is a one divided by 10?
We get a piece called a tenth. A tenth is a fraction, written as \(\dfrac{1}{10}\).
To write numbers that include these smaller pieces, we use a decimal point to separate the whole part from the fraction part.
\(35.4\) =
This number means 3 tens, 5 ones, and 4 tenths.

Definition Decimal Number
A decimal number uses a decimal point to show a value that includes parts smaller than one. We can represent a decimal number in different ways:
  • Standard Form:
    \(35.4\)
  • Expanded Form$$\begin{aligned} 3\text{ tens} &+& 5\text{ ones} &+& 4\text{ tenths} \\ 30 &+& 5 &+& \frac{4}{10}\end{aligned}$$
  • Place Value Table:
    Tens Ones . Tenths
    3 5 . 4
  • Base Ten Cubes:

Decimals on a Number Line


A number line is like a map for numbers. Decimals have their own special place on it.
  • Finding Tenths
    If we take the space between two whole numbers, like 0 and 1, and divide it into 10 equal parts, each part is one tenth (0.1).
  • Finding Hundredths
    If we "zoom in" on a small section, like the one between 0 and 0.1, and divide it into 10 equal parts, each new part is one hundredth (0.01).

Method Placing a Decimal on a Number Line
To place a decimal like 2.27 on a number line:
  1. Find the start and end points. The number 2.27 is between 2.2 and 2.3.
  2. Draw the line and divide it into 10 equal parts. Each part will represent a hundredth.
  3. Count up from the start. The marks will be 2.21, 2.22, 2.23, and so on. Find the 7th mark to place 2.27.