Question

Cynthia said that 0.0001 is bigger than 0.1 because the first number has more digits to the right of the decimal point. Is Cynthia correct? Explain your thinking using negative Powers of 10 and the number line.

Answer 1

No, Cynthia is not correct. The number with more digits to the left of the decimal point is bigger. Using negative powers of 10 and the number line, we can see that as the power of 10 becomes more negative, the value of the number decreases.

Step-by-step explanation:

No, Cynthia is not correct. When comparing 0.0001 and 0.1, the number with more digits to the left of the decimal point is bigger. In this case, 0.1 has one digit to the left of the decimal point, while 0.0001 has four digits to the left. Therefore, 0.1 is bigger than 0.0001.

Using negative powers of 10 and the number line, we can see that as the power of 10 more negative, the value of the number decreases. For example, 0.1 can be written as 1 × 10-1, while 0.0001 can be written as 1 × 10-4. Since 10-4 is smaller than 10-1, 0.1 is bigger than 0.0001.