What are Decimals?

We count using **building blocks **based on **10.**

π Our first **building block **is** 1.**

To get to the next building block, we **multiply by 10**:

1x 10=10

Each building block has a **place value **name.

1=Ones

10=Tens

100=Hundreds

1,000=Thousands

We can multiply any building block by 10 to get an even bigger block!

All **numbers **are made up of these **base 10 ****building blocks**.

πΊ **Tip:** They're called **base ****10 **building blocks, because you can multiply or divide any building block **by 10 **to get **another building block! **

Look at this whole number:

572

It's made up of base 10 building blocks! 5 **hundreds,** 7 **tens,** and 2 **ones.**

The **position **of each digit tells you its value.

As you move to the **left **π, the values of the digits become **bigger.**

As you move to the **right** π, the values of the digits become **smaller.**

We **multiply by 10 **to make **bigger** building blocks.Β

We can also **divide by 10 **to make **smaller **building blocks!

So what happens if we divide 1 by 10? Is there a smaller building block than 1? π€

When we divide 1 by 10 in math, we make a fraction:

πΊ We also make a new building block:

0.1=One tenth= 1/10

Did you notice the **period ****. ****symbol **above?Β

That's called the **decimal point!**

Building blocks that are smaller than 1 use **decimal points.**

A **decimal point **separates **whole numbers **on the left side (π) from their **fraction **parts to the right (π).

If we divide 0.1 by 10 again, we get an even smaller building block:

0.01=One hundredth

**0.01** is the same as the fraction ^{1}**/**_{100}**!**

**Tip:** The number **1 **can be written with a decimal point too, like **1.0. **We just usually skip writing the **'.0'.**

We can keep dividing building blocks by 10 to get even smaller building blocks:

0.001=One thousands

0.0001=One ten-thousands

...

Numbers further to the right π of decimal points become smaller and smaller.

Our first decimal building block is **1/10.**

Imagine a whole divided into 10 parts.

Each part is 1/10 of the whole.Β

If you add them all together, they will make 1.

This is called the **Tenths**** place.**

π€ Take note that **this is different from the ****Tens ****place.**

The **digit in the Tenths place** is the first digit we write after the decimal point.

Any number we write in this place tells us how many Tenths we're dealing with.

π Look at this number.

572.4

What is the place value of the **4?**

β
Yes, **4 **is in the **Tenths **place.

This means the place value of 4 is worth **4/10.**

Our number is...Β

572and4 Tenths

or

572and4/10

But we can just say "*five hundred seventy-two **point four**"*.Β

Let's add another digit to our number.

Let's add a 6 after the 4:

572.46

This brings us to our next building block which is **1/100.**Β

We call this the **Hundredths**** place.**

The **second digit **we write after the decimal point is in the Hundredths place.

π€ Remember that **this is different from the Hundreds place.**

Imagine a whole divided into 100 parts.

Each part is 1/100^{th} of the whole.

Our example shows that **6 is in the Hundredths place.**

This means that we're dealing with **6/100.**

So, our number is...

572+4Tenths+6 Hundredths

or

572+4/10+6/100

π But we can just say "*five hundred seventy-two **point forty-six"***.**

We can keep going further, but let's stop at the Hundredths place for now.

π Tip: Remember that as you move further to the right πππ, you **just keep on dividing by 10.**

A **decimal point **separates the **whole numbers** on the left side (π) and the place values for **fractions **on the right side (π).

The numbers **on the left **are **greater than 1.**

The numbers **on the right **are **less than 1.**

Let's look at another example.

0.94

We have **0 ones.**

After the decimal point, we see 9 and 4.

π€ What's the place value of **9?**

Yes, it's in the **Tenths place.**

It's shows us **9/10.**

π€ What's the place value of the digit after 9?

Yes! It's the **Hundredths place.**

It shows us **4/100.**

Now we have...

0 Ones+9 Tenths+4 Hundredths

**or**

0+9/10+4/100

**0.94 **is also the same as **94 hundredths**!

Or we can also say "*zero point nine four*".

**Tip: **Even if we have nothing in the Ones place, we still write a 0 before the decimal point.

**Super Tip:** **1 **can be written as **1.0**.Β

1.0 and 1 mean the same thing. For convenience, we just don't usually write the '.0'

Now, you can move on to practice. πͺ

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