Mathematical Skills for Science

Introduction

In physics as well as in physical sciences in general, there are many skills that you need to learn. These include working with units, basic mathematics skills and laboratory skills. In this lesson and the next few, we will revise some of these skills that you should know before starting to study physics and science in general.

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Mathematical Skills

You should be comfortable with scientific notation and how to write scientific notation. You should also be able to easily convert between different units and change the subject of a formula. In addition, concepts such as rate, direct and indirect proportion, fractions and ratios and the use of constants in equations are important.

Rounding Off

Certain numbers may take an infinite amount of paper and ink to write out. Not only is that impossible, but writing numbers out to a high precision (many decimal places) is very inconvenient and rarely gives better answers. For this reason we often estimate the number to a certain number of decimal places.

Rounding off a decimal number to a given number of decimal places is the quickest way to approximate a number. For example, if you wanted to round-off 2.6525272 to three decimal places then you would first count three places after the decimal. Next you mark this point with a \(|\):

\(2.652|5272.\)

All numbers to the right of \(|\) are ignored after you determine whether the number in the third decimal place must be rounded up or rounded down. You round up the final digit (make the digit one more) if the first digit after the \(|\) is greater than or equal to 5 and round down (leave the digit alone) otherwise. So, since the first digit after the \(|\) is a 5, we must round up the digit in the third decimal place to a 3 and the final answer of 2.6525272 rounded to three decimal places is 2.653.

In a calculation that has many steps, it is best to leave the rounding off right until the end. This ensures that your answer is more accurate.