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The length of a small rug is 2.5 × 10³cm and the width is 4 × 10 5 cm. If the rug is rectangular in shape, the area of the rug, using scientific notation is 4​

User TimHorton
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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.

User Amklose
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