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The thickness of a strand of cotton is about 9×10−19 \times 10^{-1} millimeters. The thickness of a strand of silk is about 3×10−23 \times 10^{-2} millimeters.\newlineUse these numbers to complete the sentence below. Write your answer in standard form, without using exponents.\newlineA strand of cotton is about ____ times as thick as a strand of silk.

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Full solution

Q. The thickness of a strand of cotton is about 9×10−19 \times 10^{-1} millimeters. The thickness of a strand of silk is about 3×10−23 \times 10^{-2} millimeters.\newlineUse these numbers to complete the sentence below. Write your answer in standard form, without using exponents.\newlineA strand of cotton is about ____ times as thick as a strand of silk.
  1. Divide Thicknesses: To find out how many times thicker the cotton is than the silk, we divide the thickness of the cotton by the thickness of the silk.\newlineSo, we do (9×10−1)/(3×10−2)(9 \times 10^{-1}) / (3 \times 10^{-2}).
  2. Divide Numbers: First, divide the numbers without the exponents: 9/3=39 / 3 = 3.
  3. Subtract Exponents: Now, subtract the exponents: −1−(−2)=−1+2=1-1 - (-2) = -1 + 2 = 1.
  4. Combine Results: Combine the results: 3×1013 \times 10^1.
  5. Final Answer: 10110^1 is just 1010, so the final answer is 3×103 \times 10, which is 3030.

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