Lesson 8: Use Powers of 10 to Estimate Quantities

Property

A power of 10 can be written in exponential form as $10^n$, where the base is 10 and the exponent $n$ indicates the number of times 10 is used as a factor. The value of the exponent $n$ is equal to the number of zeros in the standard form of the number.

Examples

Property

In decimal place value, positions to the right of the decimal point are represented by negative powers of 10:

Property

To quickly estimate a real-world quantity, round the number to its greatest place value. The estimated quantity can then be expressed in the form $d \times 10^n$, where "$d$" is a single non-zero digit (1 through 9) and "$n$" is an integer.

Examples

• Example 1: The population of a state is 8,923,567. Rounding to the greatest place value gives 9,000,000. This can be written as an estimate of 9 x 10^6.
• Example 2: The diameter of a red blood cell is approximately 0.0000075 meters. Rounding to the greatest place value gives 0.000008 meters. This can be written as an estimate of 8 x 10^-6.

Explanation

When dealing with massive data, exact numbers are often unnecessary and hard to read. This estimation method simplifies messy numbers into a highly manageable form. By rounding to the highest place value, you create a clean number with just a single digit, which you can then instantly rewrite as a power of 10.