Question

Estimate the order of magnitude (power of 10) of (a) 2800, (b)$86.30\times {10}^3$(c) 0.0076, and (d)$15.0\times {10}^8.$

Short answer

(a) The order of the magnitude of 2800 is 2.

(b) The order of the magnitude of $86.30\times {10}^3$is 4.

(c) The order of the magnitude of 0.0076 is –3.

(d) The order of the magnitude of $15.0\times {10}^8$is 9.

Significant figures are the digits that contribute to the accuracy in measurement.

Step-by-step solution

Step 1. Calculating the number of significant figures in 2800

There are two significant digits in 2800 because the last two zeroes are not significant.

Writing in scientific notation

In scientific notation, 2800 can be written as $2.8\times {10}^2$. Thus, the order of magnitude of 2800 is 2.

Step 2. Calculating the number of significant figures in 86.30×103

There are four significant digits in $86.30\times {10}^3$.

Writing in scientific notation

In scientific notation, $86.30\times {10}^3$can be written as $8.630\times {10}^4$. Thus, the order of the magnitude of $8.630\times {10}^4$is 4.

Step 3. Calculating the number of significant figures in 0.0076

There are four significant digits in 0.0076.

Writing in scientific notation

In scientific notation, 0.0076 can be written as $7.6\times {10}^{-3}$. Thus, the order of magnitude of 0.0076 is –3.

Step 4. Calculating the number of significant figures in 15.0×108

The number of significant digits in $15.0\times {10}^8$is 3.

Writing in scientific notation

In scientific notation, $15.0\times {10}^8$can be written as $1.50\times {10}^9$. Thus, the order of magnitude of $15.0\times {10}^8$is 9.