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# Scientific Notation for Physics Help

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By McGraw-Hill Professional
Updated on Sep 17, 2011

## Introduction

You should know about scientific notation , the way in which physicists and engineers express the extreme range of values they encounter. How many atoms are in the earth? What is the ratio of the volume of a marble to the volume of the sun? These numbers can be approximated pretty well, but in common decimal form they are difficult to work with.

Scientists and engineers like to express extreme numerical values using an exponential technique known as power-of-10 notation . This is usually what is meant when they talk about “scientific notation.”

## Standard Form

A numeral in standard power-of-10 notation is written as follows:

m.n × 10 z

where the dot (.) is a period written on the baseline (not a raised dot indicating multiplication) and is called the radix point or decimal point . The value m (to the left of the radix point) is a positive integer from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. The value n (to the right of the radix point) is a non-negative integer from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. The value z , which is the power of 10, can be any integer: positive, negative, or zero. Here are some examples of numbers written in standard scientific notation:

2.56 × 10 6

8.0773 × 10 −18

1.000 × 10 0

## Alternative Form

In certain countries and in many books and papers written before the middle of the twentieth century, a slight variation on the preceding theme is used. The alternative power-of-10 notation requires that that m = 0 rather than m = 1. When the preceding quantities are expressed this way, they appear as decimal fractions larger than 0 but less than 1, and the value of the exponent is increased by 1 compared with the standard form:

0.256 × 10 7

0.80773 × 10 −17

0.1000 × 10 1

These are the same three numerical values as the previous three; the only difference is the way in which they’re expressed. It’s like saying that you’re driving down a road at 50,000 meters per hour rather than at 50 kilometers per hour.

Practice problems for these concepts can be found at: Scientific Notation for Physics Practice Test

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