Chapter 1, Problem 24P

(a)

To determine

The order of magnitude (power of 10) of2800.

Answer to Problem 24P

Solution: ${10}^3$

Explanation of Solution

Here, the number is to be converted to the power of 10 keeping in mind that the decimal is right to the leftmost non-zero number: $2.8\times {10}^3$ .

Thus, the order of magnitude is ${10}^3$ .

Conclusion:Estimated order of magnitude (power of 10) is ${10}^3$ .

(b)

To determine

The order of magnitude (power of 10) of: $86.30\times {10}^3$

Answer to Problem 24P

Solution:

${10}^4$

Explanation of Solution

Here, the number is to be converted to the power of 10 keeping in mind that the decimal is right to the leftmost non-zero number: $8.630\times {10}^4$. Thus, the order of magnitude is ${10}^4$ .

Conclusion:Estimated order of magnitude (power of 10) is ${10}^4$.

(c)

To determine

The order of magnitude (power of 10) of0.0076.

Answer to Problem 24P

Solution: ${10}^{(-3)}$

Explanation of Solution

Here, the number is to be converted to the power of 10 keeping in mind that the decimal is right to the leftmost non-zero number: $7.6\times {10}^{(-3)}$ .

Thus, the order of magnitude is ${10}^{-3}$ .

Conclusion:

Estimated order of magnitude (power of 10) is ${10}^{-3}$ .

(d)

To determine

The order of magnitude (power of 10) of: $15.0\times {10}^9$

Answer to Problem 24P

Solution: ${10}^{10}$

Explanation of Solution

Here, the number is to be converted to the power of 10 keeping in mind that the decimal is right to the leftmost non-zero number: $1.50\times {10}^{10}$ .

Thus, the order of magnitude is ${10}^{10}$ .

Conclusion:

Estimated order of magnitude (power of 10) is 10¹⁰.