Final answer:
While Sandy's method works for multiplying by 100, Bobby's example of multiplying by 10 is not the correct way to demonstrate the flaw. To multiply by 100, move the decimal two places to the right and use zeros as placeholders if needed. Understanding the use of placeholders and the movement of decimal points is key to multiplying and dividing by powers of ten.
Step-by-step explanation:
Sandy's claim that when you multiply a number by 100, you can just write a 00 at the right end of the number is correct in the context of whole numbers and decimals where the number of digits to the right of the decimal place is exactly two. However, Bobby's example of 0.5 x 10 to refute Sandy's claim does not directly relate to Sandy's statement about multiplying by 100. Instead, Bobby's example involves multiplying by 10, which would require moving the decimal point one place to the right, resulting in 5, not 50.
To understand multiplying by 100 correctly, it's essential to grasp that you're essentially moving the decimal point two places to the right. When there are not enough digits to the right of the decimal point after multiplication, zero placeholders are added. For instance, 2.4 x 100 requires moving the decimal two places to the right. Since there's only one number after the decimal, a zero is added to make 240.
Multiplying and dividing by tens is a fundamental concept where decimal places and zero placeholders play a crucial role. The ability to move the decimal point in both directions is necessary to handle various exponents correctly, whether the number is being multiplied or divided by powers of ten.