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Arrange the numbers in each set below in order from smallest to largest. Hint: You need to rewrite the numbers so that they have the same power of ten. Set (i): (a) 3.23 × 10^6 (b) 99.8 × 10^4 (c) 0.301 × 10^7 (d) 115 × 10^5 Set (ii): (a) 10^5. × 10^-4 (b) 0.0125 × 10^1 (c) 7.64 × 10^-2 (d) 932 × 10^-5

Answer :

Final answer:

The student is asked to order numbers from smallest to largest, rewritten in scientific notation. Following the powers of 10, we arrange the numbers in each set accordingly.

Explanation:

The subject here is about organizing numbers expressed in scientific notation. This is accomplished by comparing the exponents of 10, since the power (exponent) of 10 indicates the number of decimal places shifted to give the digit number. Let's sort the digits in each set:

  1. Set (i): From smallest to largest we have: [tex](b) 99.8 × 10^4 = 9.98 × 10^5, (d) 115 × 10^5 = 1.15 × 10^7, (a) 3.23 × 10^6 = 3.23 × 10^6, (c) 0.301 × 10^7 = 3.01 × 10^6[/tex]
  2. Set (ii): From smallest to largest, we have: [tex](d) 932 × 10^-5 = 9.32 × 10^-3,[/tex][tex](c) 7.64 × 10^-2 = 0.0764 × 10^0,[/tex][tex](b) 0.0125 × 10^1 = 0.125 × 10^0,[/tex] [tex](a) 10^5 × 10^-4 = 1 × 10^1[/tex]

Remember, scientific notation simplifies arithmetic, especially when dealing with very large or very small numbers.

Learn more about Scientific Notation here:

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