what is the product of 7.5 and 1000
what is the product of 7.5 and 1000
The Correct Answer and Explanation is:
The product of 7.5 and 1000 is 7500.
Explanation
To find the product of 7.5 and 1000, we simply perform a multiplication operation:7.5×1000=75007.5 \times 1000 = 75007.5×1000=7500
This result can be confirmed through several methods, including breaking the numbers down or visualizing them in terms of place value.
Understanding the Multiplication:
The number 7.5 is a decimal number, meaning it includes a whole number (7) and a fraction (0.5). The number 1000 is a whole number that represents a large value often used in scaling or grouping. When we multiply a decimal number by a power of 10 (like 1000), we effectively shift the decimal point to the right.
Mathematically, multiplying 7.5 by 1000 means:7.5×103=75007.5 \times 10^3 = 75007.5×103=7500
This works because each multiplication by 10 shifts the decimal one place to the right:
- 7.5×10=757.5 \times 10 = 757.5×10=75
- 7.5×100=7507.5 \times 100 = 7507.5×100=750
- 7.5×1000=75007.5 \times 1000 = 75007.5×1000=7500
Why Is This Useful?
Multiplying decimals by powers of 10 is a fundamental concept in arithmetic, often used in real-life scenarios. For example:
- If you earn $7.50 an hour and work 1000 hours, you will earn $7500.
- If a product costs $7.50 and you buy 1000 units, your total cost is $7500.
This also shows how decimals can scale up to large values. It reinforces the idea that place value is critical in understanding the base-10 number system, and it gives us tools to estimate and calculate in finance, science, and engineering.
In summary, the product of 7.5 and 1000 is 7500, and this operation is a practical example of scaling a decimal number by a power of ten.
