Final answer:
Sarah is incorrect; 0.00001 is smaller than 0.001. The value of a number is determined by its place value - not the number of digits. Scientific notation and a number line confirm that 0.001 has a greater value due to its higher power of ten position.
Step-by-step explanation:
The statement by Sarah that 0.00001 is bigger than 0.001 is incorrect because the value of a number with digits to the right of the decimal point is determined by the place value of the first non-zero digit. Even though a number may have more digits, it does not necessarily mean it is greater. Here's how to understand this with the powers of ten and using a number line.
Using Powers of Ten
When we use scientific notation, we express numbers as a digit times a power of ten. For example, 0.001 can be written as 1 × 10-3. This means the decimal point is moved three places to the left. Similarly, 0.00001 can be written as 1 × 10-5 which indicates the decimal point is moved five places to the left. Since 10-3 is larger than 10-5, we can conclude that 0.001 is larger than 0.00001.
Using a Number Line
On a number line, numbers to the right are always larger than numbers to the left. 0.001 would be placed to the right of 0.00001 on the number line, indicating that it is the greater number. It is the position of the number relative to others, not the quantity of digits, that determines its size.