The question is asking for three different ways to name the number 41.06. Let's break down each option:

1. 4,106 hundredths:

   • 41.06 is equivalent to 4,106 hundredths because: $41.06 = \frac{4106}{100}$ So, this option is correct.

2. 4 tens + 106 hundredths:

   • 41.06 can be written as: $4 \text{ tens} = 40 \quad \text{and} \quad 106 \text{ hundredths} = 1.06$ Adding them gives $40 + 1.06 = 41.06$, so this option is correct.

3. 4 tens + 1 ones + 6 tenths:

   • 41.06 can be written as: $4 \text{ tens} = 40, \quad 1 \text{ one} = 1, \quad \text{and} \quad 6 \text{ tenths} = 0.6$ Adding these gives $40 + 1 + 0.06 = 41.06$, so this option is correct.

4. 410 tenths + 6 hundredths:

   • $410 \text{ tenths} = 41.0$ and $6 \text{ hundredths} = 0.06$, so $41.0 + 0.06 = 41.06$, making this option correct.

5. 41 tens + 6 hundredths:

   • $41 \text{ tens} = 410$ and adding $6 \text{ hundredths} = 0.06$ would give $410.06$, which is incorrect. So this option is wrong.

Correct answers:

• 4,106 hundredths
• 4 tens + 106 hundredths
• 4 tens + 1 ones + 6 tenths

Would you like further details on decomposing decimals or have any other questions? Here are five related questions to extend your learning:

1. How do you convert a decimal number into hundredths?
2. What are different ways to represent decimals in expanded form?
3. Can you explain how place value changes with tenths, hundredths, and thousandths?
4. How do you convert between fractions and decimals?
5. How do you round decimals to the nearest tenth or hundredth?

Tip: When decomposing decimals, focus on the value of each place (tenths, hundredths, etc.) to get an accurate representation!