Answer: To find the area of a rectangular rug, we need to multiply the length and the width. The length of the rug is 2.5 × 10³ cm and the width is 4 × 10⁵ cm. Using scientific notation, we can write:
Area=(2.5×103)×(4×105)
To multiply two numbers in scientific notation, we need to multiply the coefficients and add the exponents. The coefficient of the product must be between 1 and 10. The steps are as follows:
Multiply the coefficients: 2.5 × 4 = 10
Add the exponents: 3 + 5 = 8
Write the product in scientific notation: 10 × 10⁸
Adjust the coefficient if needed: Since 10 is not between 1 and 10, we need to move the decimal point one place to the left and increase the exponent by one. The final answer is:
Area=(1×101)×(1×108)=1×109
Therefore, the area of the rug, using scientific notation, is 1 × 10⁹ cm².