1. Which expression shows 30.21 in expanded form? A. \( (3 \times 1)+\left(2 \times \frac{1}{1}\right)+\left(1 \times \frac{1}{10}\right) \) B. \( (3 \times 10)+\left(2 \times \frac{1}{1}\right)+\left(1 \times \frac{1}{10}\right) \) C. \( (3 \times 10)+\left(2 \times \frac{1}{10}\right)+\left(1 \times \frac{1}{100}\right) \) D. \( (3 \times 1)+\left(2 \times \frac{1}{10}\right)+\left(1 \times \frac{1}{100}\right) \)
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To express 30.21 in expanded form, we need to break it down into its components based on place value. The number 30.21 consists of 30, 0.2, and 0.01. Therefore, we can represent it like this: 30 = \(3 \times 10\) (3 is in the tens place) 0.2 = \(2 \times \frac{1}{10}\) (2 is in the tenths place) 0.01 = \(1 \times \frac{1}{100}\) (1 is in the hundredths place) So, the correct expression that shows 30.21 in expanded form is: **C. \( (3 \times 10) + \left(2 \times \frac{1}{10}\right) + \left(1 \times \frac{1}{100}\right) \)** Engaging with numbers can be so much fun! Just think of them as building blocks where every digit has its own special place. It’s like a treasure map, guiding you through the land of mathematics, where every little part counts! To avoid common mistakes, always check the place value of each digit before expanding. It can be easy to confuse tenths with hundredths! Remember, the bigger the place, the bigger the multiplier you use. Making a visual chart can also help reinforce these concepts—it's like turning math into art!
