QuestionWhen you multiply 104.3 by 10, it shifts the decimal right to 1,043. Why does multiplying by 0.10 shift it to 10.43?
Studdy Solution
STEP 1
Assumptions1. The original decimal number is104.3. When multiplied by10, the decimal number becomes1,0433. When multiplied by0.10, the decimal number becomes10.43
STEP 2
First, let's understand what happens when a decimal number is multiplied by10. Multiplying by10 shifts all digits one place to the left, moving the decimal point one place to the right.
STEP 3
Now, let's understand what happens when a decimal number is multiplied by0.10. Multiplying by0.10 is the same as dividing by10, which shifts all digits one place to the right, moving the decimal point one place to the left.
STEP 4
The reason why these operations work as they do is because of the place value system in decimal numbers. Each place to the left of the decimal point represents a power of10 (10,100,1,000, etc.), and each place to the right of the decimal point represents a negative power of10 (1/10,1/100,1/1,000, etc.).So, when we multiply by10, we're increasing the power of10 for each digit, effectively shifting them one place to the left. Conversely, when we multiply by0.10, we're decreasing the power of10 for each digit, effectively shifting them one place to the right.
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