Chapter 4, Problem 14CST

To determine

To order the lengths from least to greatest

Answer to Problem 14CST

  $2.5\times {10}^{-6},7.5\times {10}^{-6},18\times {10}^{-6}$

Explanation of Solution

Given information:

Three lengths of bacteria −

  $0.000018$

  $7.5\times {10}^{-6}$

  $2.5\times {10}^{-6}$

Formula Used: Exponents Comparison

Calculation:

To arrange the numbers in order, need to make the exponents for all numbers same. For two numbers, the exponent of 10 is -6.

Let us change the first length $0.000018$ into scientific notation.

To convert to scientific notation, move the decimal point to the left (or right side). In the given number, the decimal is to be moved to the right side. Whenever the decimal is required to be moved to the right side, the exponent becomes negative.

So, here in the given number $0.000018$ - start moving the decimal point to the right. As there are 4 zero’s, may first write the number as-

  $=0.18\times {10}^{-4}$

As need to change the exponent to -6, move the decimal to the right by two more points to have

  $18\times {10}^{-6}$

Since the exponent is same for all three numbers-

  $18\times {10}^{-6}$

  $7.5\times {10}^{-6}$

  $2.5\times {10}^{-6}$

now compare the numbers 18 , 7.5 and 2.5.

  $18>7.5>2.5$

So the final sequence from least to greatest is −

  $2.5\times {10}^{-6},7.5\times {10}^{-6},18\times {10}^{-6}$

Conclusion-

  $2.5\times {10}^{-6},7.5\times {10}^{-6},18\times {10}^{-6}$