Let's break down the task in the image step by step:

Problem:

You need to find three rational numbers between each pair of numbers and then sketch a number line to represent them.

a) Numbers between 3.3 and 3.4:

Rational numbers are any numbers that can be expressed as fractions or decimals that terminate or repeat. Since 3.3 and 3.4 are decimals, we can pick numbers between them.

Three rational numbers between 3.3 and 3.4 could be:

• 3.31
• 3.32
• 3.35

These numbers are simple, terminating decimals, so they are all rational.

b) Numbers between -2.26 and -2.25:

Here, the numbers are negative, but the idea is the same. We pick rational numbers between these two values.

Three rational numbers between -2.26 and -2.25 could be:

• -2.255
• -2.258
• -2.259

These are also terminating decimals, so they qualify as rational numbers.

Number Line:

You would sketch two separate number lines for each part of the question.

1. For part (a), draw a line starting from 3.3 and ending at 3.4, marking the rational numbers 3.31, 3.32, and 3.35 between them.
2. For part (b), draw a line from -2.26 to -2.25, marking -2.255, -2.258, and -2.259 between them.

Would you like me to create these number lines visually for you?

Follow-up Questions:

1. What other rational numbers could you choose between 3.3 and 3.4?
2. How can you determine if a decimal is rational or irrational?
3. What distinguishes rational numbers from irrational numbers?
4. Can fractions also be used as rational numbers between two decimals?
5. How would you represent irrational numbers on a number line?

Tip:

When dealing with rational numbers, remember that any terminating or repeating decimal is a rational number.