QuestionWhen multiplying by a power of 10, how do digit shifts relate to zeros in the power? Give an example.
Studdy Solution
STEP 1
Assumptions1. We are multiplying a number by a power of10. The power of10 is represented as10^n, where n is a positive integer3. The number of places the digits move is the same as the number of zeros in the power of10
STEP 2
Let's start with a simple example to illustrate the concept. Let's multiply5 by10, which is a power of10 with one zero.
STEP 3
As we can see, the digit5 has moved one place to the left, which is equivalent to the number of zeros in10.
STEP 4
Now, let's try a larger power of10. Let's multiply by100, which is a power of10 with two zeros.
STEP 5
Again, the digit5 has moved two places to the left, which is equivalent to the number of zeros in100.
STEP 6
From these examples, we can conclude that when a number is multiplied by a power of10, the number of places the digits move to the left is the same as the number of zeros in the power of10.
So, the relationship between the number of places the digits move and the number of zeros in the power of10 is that they are equal.
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