Sequences with Decimals

We use decimals in real life all the time! πΊ

We use decimals to count money,

to read price lists,

and even to take measurements like temperature, length, volume, and weight!

We usually use **decimal sequences** when we deal with these things.

What exactly is a decimal sequence? π€

A **decimal sequence **is just a sequence of decimals. In other words, a decimal sequence is **a set of decimals that make a pattern**.Β

Like all sequences, decimal sequences have a **rule **that tells us how to go from one number to the next.

This is an example of a decimal sequence:

3.1,3.2,3.3,?,3.5,3.6,3.7

How do we find the missing number?Β

**π First,** **figure out the ****rule **of the sequence.

To find the **rule**, take **any two numbers next to each other**. Then **subtract **the smaller number from the larger number.

The difference between the two numbers helps you figure out the rule.

In our example, 3.1 and 3.2 are next to each other.Β

Let's subtract:

3.2 - 3.1 =0.1

To be sure that this is our rule, let's subtract another pair of numbers in the pattern.

3.6 - 3.5 =0.1

The difference between numbers is **0.1 **too!

Thispatternhas adifference of 0.1 between numbers.

**π Now, let's ****figure out the ****rule **for the sequence.

If the **numbers are increasing,** then the rule is to **add **the difference.

If the **numbers are decreasing,** then the rule is to **subtract ****the **difference.

Did you figure out the rule for the sequence? π€

We see that the numbers are increasing.

Sothe rule istoadd 0.1to get the next number.

Let's complete the sequence now.

The number before the missing number is 3.3.

If we **add 0.1** to that, we get 3.4.

3.3 + 0.1 =3.4

The missing number is 3.4!

3.1,3.2,3.3,3.4,3.5,3.6,3.7

To see if our answer is correct, let's subtract 3.4 from 3.5.

3.5 - 3.4 =0.1

The difference matches our pattern! π

Here's another sequence:

7.4,7.2,6.8,6.6,6.4,?

Can you figure out the missing number?

π **Figure out the rule **by subtracting 2 numbers that are next to each other.

Let's take 6.4 and 6.6.Β

Let's subtract:

6.6 - 6.4 =0.2

Let's subtract another pair of numbers that are next to each other:

7.4 - 7.2 =0.2

The difference between numbers is **0.2**.

Thepatternhas adifference of 0.2 between numbers. The next numberdecreases by 0.2.

Did you figure out the **rule?** π€

Is it...

**Add 0.2 **to get the next number?

No, it's not.Β

The numbers are not increasing.

Is it...

**Subtract 0.2**?

Yes! The numbers are getting smaller, so we subtract.

Ourruleis tosubtract 0.2to get the next number.

Now let's go back to our decimal sequence:

7.4,7.2,6.8,6.6,6.4,?

What comes after 6.4? Let's use our rule:

6.4-0.2=6.2

So the next number is 6.2! π

Just to be sure, we'll check by getting the difference between 6.2 and 6.4.

6.4 -6.2=0.2

It matches our pattern. π

Nice work! ππ

Complete more sequences by doing practice. ππͺ

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