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# Decimals and Place Values

### Decimals and Place Values

Decimals are another way to represent numbers which are not whole. They also have place values.

This is a number line

In-between the whole numbers (the integers), there are numbers slotted in that are not whole.

These numbers that are not whole numbers are called _________ numbers.

So what do you think you call the "dot" in decimal numbers?

A) Number point B) Decimal point

So decimal numbers are numbers in-between whole numbers

This lesson focuses on how much the ciphers after the decimal point are actually worth.

For example, how much is the $7$ worth in $0.478$?

First of all, though!

Have a look at the place values of the numbers **before** the decimal point.

What is the place value of the $4$ in this example?

A) $1,000$ B) $100$ C) $10$

How much is the $4$ "worth" then?

What is the place value of the $7$?

A) $1$ B) $10$ C) $100$

True or false? *Every time you move one place value to the left, the place value gets* $100\times$ *larger.*

Every time you move one place value to the left, the value gets $10 \times$ larger

**Tens** are $10\times$ larger than units.
**Hundreds** are $10\times$ larger than tens.
**Thousands** are $10\times$ larger than hundreds.

Now, how about the place value of the decimals?

**Decimals** are the numbers after the decimal point.

True or false? *The* $5$ *in this number has place value* $1,000$ *just like the* $4$*?*

The $5$ has place value $\frac{1}{1,000}$ or "one thousandth"

The $4$ on the left-hand-side of the decimal point has place value **thousand**, so it is worth $4,000$

The $5$ on the right-hand-side of the decimal point has place value **thousandth**, so it is only worth $0.005$

Is the place value for the $1$ bigger or smaller than the place value for the $5$?

A) Bigger B) Smaller

What place value does the $1$ have?

A) $\frac{1}{10}$ B) $\frac{1}{100}$

What is the place value for the $2$?

Every time you move one place value to the *right*, the place value gets $10\times$ ___________.

A) larger B) smaller

So the place values are smaller than $1$ on the right-hand-side of the decimal point

1 **tenth** is the same as $\frac{1}{10}$
1 **hundredth** is the same as $\frac{1}{100}$
1 **thousandth** is the same as $\frac{1}{1,000}$

How many tenths are there in this decimal number?

How many hundredths are there in this decimal number?

How many thousandths are there in this decimal number?

So $0.472$ has...

4 tenths. 47 hundredths. 472 thousandths.

How many **hundredths** are there in the decimal number $0.025$?

How many tenths are in the decimal number $0.379$?

How do you write **34 hundredths** as a decimal number?

How do you write **583 thousandths** as a decimal number?

Now! How do you write **23 thousandths** as a decimal number?

Which one is the **biggest** decimal number?

Which one is the **biggest** decimal number?

Summary! Decimal numbers are numbers in-between whole numbers

**Decimals** are the numbers that follow the **decimal** **point**.

Decimals have place values

The first decimal has **place** **value** $\frac{1}{10}$ (1 tenth).
The second decimal has **place** **value** $\frac{1}{100}$ (1 hundredth).
The third decimal has **place** **value** $\frac{1}{1,000}$ (1 thousandth).

Place values change by $10\times$ when you move left or right

They get $10 \times$ **bigger** every time you move one place **left**.
They get $10 \times$ **smaller** every time you move one place **right**.