There are three main significant digits rules that every student needs to keep in mind when performing calculations and determining the number of significant figures in a number:

- Non-zero digits are always significant.
- Zeros between non-zero digits are significant.
- A zero or zeros at the end of a non-decimal or a decimal are significant.

Significant digits (figures) are the digits that contribute to the accuracy of the value and help round numbers correctly.

** Example 1**: in the number

**45032**all digits are significant since 0 is between other non-zero digits.

In order to round this number to the first significant digit, we look at the first significant digit **4** and then at the value of the digit next to it **5**. Since the value of the digit next to the first significant digit is 5 or higher, rounding to the first significant digit would be **up**: *5000*.

** Example 2**: in the number 0.000745 zeros are not significant. The first significant digit here is

**7**and the last is

**5**. Rounding this number to the first significant digit would mean taking

**7**, looking at the digit next to it,

**4**, and since

**4**is less than

**5**, then the number is rounded

**down**:

*0.000700*. Note that now the

**zeros**following the

**7**are significant, because they show the value of the number more accurately.

** Example 3**: when multiplying and dividing numbers, check how many significant digits each number has.

45.23 has 4 significant digits

2.1 has 2 significant digits.

The final answer (the product or the quotient of the two numbers) will have the **least** number of significant figures within any number in the problem.

So, if we multiplied 45.23 and 2.1 we would keep **two** significant digits in the answer.

** Example 4**: when adding and subtracting numbers, check how many significant digits exist in the decimal part of each number. Then add/subtract the numbers as usual and in the sum/difference keep the least number of significant figures from each number in the problem in the decimal portion of the answer.

**67.03** has **2** significant digits in the decimal portion

**6.483** has **3** significant digits in the decimal portion

When added together, the answer would contain** 2** significant digits in the decimal portion.

The importance of significant figures was established in the 18th century A.D., when scientists realized the need to have more accurate solutions and made a connection between rounding and the incorrect final results. A German mathematician Carl Friedrich Gauss studied how significant digits rules were affecting the calculations.

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