The movement of the decimal point when multiplying by 10 or 0.1 is related to how these operations affect the value of a number.
-
Multiplying by 10: When you multiply a number by 10, you are increasing its value tenfold. This is equivalent to moving the decimal point one place to the right. For example:
- \(3.2 \times 10 = 32\) (moving the decimal one place right)
- \(0.45 \times 10 = 4.5\) (again, moving the decimal one place right)
This movement to the right reflects that each digit's value is increasing by a factor of ten (e.g., the '3' in '3.2' becomes '30', and the '2' becomes '0').
-
Multiplying by 0.1: When you multiply a number by 0.1, you are decreasing its value to one-tenth of that number. This corresponds to moving the decimal point one place to the left. For example:
- \(3.2 \times 0.1 = 0.32\) (moving the decimal one place left)
- \(0.45 \times 0.1 = 0.045\) (moving the decimal one place left)
Moving the decimal left reflects that each digit's value is decreasing by a factor of ten, making the number smaller.
In summary, moving the decimal right or left corresponds to the multiplication effects of scaling the number up or down by powers of ten.
1 answer