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# Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

## Why They're Important?

Significant digits (sometimes called significant figures or abbreviated to sig digs/sig figs) are a way of ensuring that we are calculating numbers to the correct amount of precision. For example, when we are taking measurements in a laboratory, we want to make sure that any calculation we do on those measurements are precise, and we can do this by using significant digits. Significant digits are particularly important in engineering, chemistry, physics and many other sciences as these areas require number precision throughout calculations.

## How to Find Significant Digits

We start counting the number of significant digit at the leftmost non-zero value of the number and we stop counting after the rightmost number (which could be a 0)

Examples:

1) $$50.0$$ has three significant digits since we start counting at the 5 and move right

2) $$3.9$$ has two significant digits since we start counting at the 3 and move right

3) $$0.00056$$ has two significant digits since we start counting at the 5 and move right

4) $$8.432∗10^{-6}$$ has four significant digits since we start at the 8 of the $$8.432$$ and move right

When a number has zeros before we start counting the significant digits, we call those "leading zeros". It's important to remember that leading zeros are not significant. Example #3 above has 4 leading zeros.

## Multiplication and Division with Significant Digits

When multiplying or dividing numbers with significant digits, the answer should have the same number of significant digits as the number with the least significant digits being operated on.

Example:

Solve $$4.5∗89.3$$ with the correct amount of significant digits.

Solution

$$4.5∗89.3\=401.85) However, our answer must have the least amount of significant digits of \(4.5$$ and $$89.3$$: two significant digits.

We can convert this into scientific notation to have two significant digits:

$$4.0∗10^2$$ is our final answer.

## Addition and Subtraction with Significant Digits

When adding or subtracting numbers of significance, we pay less attention to the total significant digits and more attention to the significant digits of only the decimals of the numbers. The decimal significant digits of the answer will have the least significant digits in the decimal portion of the numbers being operated on.

Example:

Solve $$89.901−7.1$$ with the correct amount of significant digits.

Solution

$$89.901−7.1=82.801$$

However, our answer must have the least amount of significant digits just in the decimal place of $$89.901$$ and $$7.1$$: one significant digit.

Since we need our answer to have only one significant digit in the decimal place, our final answer is $$82.8$$.