The operation of moving the decimal point when multiplying by 10 or 0.1 is related to how these numbers scale values.
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Multiplying by 10: When you multiply a number by 10, you are increasing its value tenfold. In the decimal system, each place value is ten times greater than the place value to its right. For example, in the number 25.3:
- The 2 is in the tens place (20),
- The 5 is in the ones place (5),
- The 3 is in the tenths place (0.3).
When you multiply 25.3 by 10, you effectively shift each digit one place to the left, making 25.3 become 253.0. This is equivalent to moving the decimal point one position to the right.
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Multiplying by 0.1: Conversely, multiplying by 0.1 means you are taking one-tenth of the number, which decreases its value. So, for the same number 25.3:
- When you multiply it by 0.1, you shift the digits one place to the right (effectively dividing by 10), resulting in 2.53. Here, moving the decimal point one position to the left reduces the value as intended.
In summary, moving the decimal point to the right multiplies the value by 10 (increasing it), while moving it to the left multiplies the value by 0.1 (decreasing it). The decimal point's movement reflects the increase or decrease in the number's magnitude based on the scale of multiplication you're applying.