Significant figures are also known as the significant digits. These are the numbers of digits in a value, often a measurement, that contribute to the degree of accuracy of the value.

# Sig Fig Calculator

## It’s All About Significant Figures

As the name indicates, significant figures are SIGNIFICANT. These are numbers that add value to number. Numbers are rounded to prevent repetition hence it is important to be careful and precise. Sig fig calculator can help you convert any number to significant figure and it can also solve your calculation problem for you.

## Decimal Numbers:

We use decimal numbers in measurement. Like 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9. From 1 to 9 ,all are significant figures, it is also called non zeroes digits .But for zero. We have to follow some rules.

## Coding OR Rules of Significant Figures:

### The Trapped Zeros:

The zeroes which are in between the non-zeroes digits are called trapped zeroes.

Example: 0.01006, there are four significant figures. ‘1006’.

### The Leading Zeros:

The zeroes that are at the beginning of the measurement are called Leading zeroes. These zeroes are never significant.

Example: 0.00230, there are 3 significant figures ‘230’.

### Trailing Zeros:

The zeroes that are in the last of the measurement are called Trailing zeroes.

If the decimal point is there in the measurement. So, it is counted as a significant figure.

Example: 600.00, there are 5 significant figures because the decimal point is given in the measurement.

In another case, if the decimal point is not there in the measurement. So the zero cannot be counted as a significant digit.

Example: 37, 000

This value is ambiguous, it is not clear whether it is measured exactly 37,000

Maybe it is measured to the nearest one, and got an exact number, got exactly 37,000, or maybe it is only measured to the nearest thousand. So, there is a little bit of ambiguity here. In this case, there is not complete information because the decimal point is not here. So, there are only 2 significant figures. ‘37’.

Here are also the example of zero: 2.5010-5 and 5.500 1012. The zeroes that are in bold faces are significant.

## Rules of Significant Figures without a decimal point:

- On the FIRST non-zero digit, start counting for sig. figs.
- On the LAST non-zero digit, stop counting for sig. figs.
- Non-zero digits are always significant.
- Zeroes in between two non-zero digits are significant.
- All the zero to the left of decimal which are less than 1 are not significant.
- Trailing zero placeholders are also not significant.
- Non zero number – all of them are significant
- In case a number have more than the desired number, it will be rounded. For example 514,000 will be significant to 3 significant numbers.
- If a value have zero at the end, it will not be removed as it will change the value of the number. Taking the same example, we cannot remove all the zero from 514,000 as it will change the whole value. What we can do in this case is to change the number into scientific notation.

## Importance of Significant Figures:

- Significant figures are important to show the exactitude of the answer.using significant figures allow the scientist and engineers to know how accurate the answer is and how much changeability there is.
- Significant digits are important when using mathematics in certain fields so that you know how precise a measurement is. If you can only measure something to the nearest 10 meters or so you would write the number like 130 or 3540 but if you can go to the nearest meter you would go to 130. or 3540.Basically signaling how precise the measurement is. This is very necessary especially when doing lots of calculations So, you don’t take for granted that you have more or less precise measurements than you do and make errors or bad perceptions based on that.

Here are the list of reasons significant figures are so useful and popular.

- Precision
- Ease of calculation
- No repetition

Significant figures indicate the precision of the answer that’s why they are important in the field of engineering and science. Measuring devices are never 100% precise so it is important that the results are shown in the value that are easy to read. Significant figures help you to know how much uncertainty there is and how precise is your answer.

Let’s go through this concept with an example. A mass of your object is 35kg and it multiplied by gravity (9.81). The weight is the product of mass and gravity.

\( Mass × Gravity = Weight \)

\( 35 × 9.81 = 343.35 N \)

Now this answer is pretty confusion as it indicate that the weight is precisely 343.35 N where it can be 345.3 as there are chances that the device was not standardized and was unable to calculate the mass accurately. Using significant figure can help in eliminating misunderstanding and provide a precise and easy to understand figure.

## Level of Accuracy:

Mathematicians or scientists who speak unlike languages agree on one common way of writing a measurement down and its having the level of accuracy behind that measurement that is easily understood by all. The foremost idea behind “significant figures” is to get everyone in the world. It is an accord that everyone says yes to use so that there is no confusion when one person reads another person’s work. There are a hundred different ways to represent accuracy in the measurement.but the above strategy is the simplest way to get the accuracy in the measurement.

## How does our sig fig calculator work?

Our sig fig calculator works in two manners. It performs arithmetic operations on multiple numbers (for example 6.38 / 4.99) or simply rounds a number to the aspiration numbers or significant figures.Just enter the number that you desire to have formatted with significant figures and the calculator will display the result.

## How To Use Sig Fig Calculator?

We designed the sig fig calculator in such a way that it can work in two modes. It can perform arithmetic operation related to multiple numbers \( \dfrac{3.16 }{ 1.122 } \) and it can also round a number to a significant figure. As we have already explained the rules, let’s try to understand them with examples. For example you have 0.003219 number and want 2 significant figures, the new value will be 0.0032. As the trailing zeros are placeholder, we don’t have to count them, then we are rounding off 3219 to 2 digits which will provide us with a new value i.e. 0.0032.

You can also use this calculator not non-decimal values. Suppose you are working with 1,234,512 as your value and want 4 significant figures, you are simply going to round off the whole value to the nearest thousand in this case and the result will be 1,235,000.

In case a number is in scientific notation, the same rules will be applied. While dealing with estimation, it is important that the significant number take the log base 10 of the sample size and rounded to the nearest integer.

**An Example**

**Rounding the Number 405.358**

Rounded To How Many sf Or df | Rounded to Significant Figures (sf) | Rounded to Decimal Figures (df) |

0 | — | 405 |

1 | 400 | 405.3 |

2 | 410 | 405.35 |

2 | 405 | 405.358 |

3 | 405.3 | 405.3580 |

4 | 405.35 | 405.35800 |

5 | 405.358 | 405.358000 |

## Modes Of Significant Figures:

We can calculate significant figures by hand or by using the sig fig calculator. For instance, we have the digits 0.003563 and want 2 significant figures. The trailing zeros are placeholders, so we do not count them. Next we round 3563 to 2 digits, leaving us with 0.0036.

Now we will consider an example that is not a decimal. Suppose we want 2,452,528 to 4 significant figures. We simply round the full number to the nearest thousand, giving us 2,453,000.

## Significant Figures In Addition and Subtraction:

There are rules regarding the operations – Addition, Subtraction.

When performing the operation \( 14.12 + 3.42 – 0.45 \), the value with the least number of significant figures (2) is 0.45. Hence, the result must have two significant figures as well: \( 14.12 + 3.42 – 0.45 = 17.09 = 17 \).The result of an operation cannot have more significant figures that the value with the least number of significant figures.

## Significant Figures In Multiplication and Division:

In this case, it is sufficient to do all calculations at once and apply the significant figures rules to the end of the result.If performing only division and multiplication.

Example: \( x = \dfrac{ 16.12 × 2.10 }{ 4.6 } = 2.793913 \).

The round off value is \( 2.8 \)

## Mixed Calculation:

Here we do mixed calculation Addition, Subtraction, Multiplication and Division.

Example: \( \dfrac{6.12 – 3.6 × 2.45}{3.2} \), After first step you will obtain \( \dfrac{6.12 – 8.82}{3.2} \) and in the second step you got \( 6.12 – 2.75625 \) and then \( 3.36375 \).

Now simply round the result leaving the last to significant figures.3.363 =3.4

## Our Sig Fig Calculator – Why Are We Proud Of It

We can understand that calculation is hard and it is important to get correct answer. So we designed a product that can solve your equations for you and provide you with an accurate result every time. No matter how difficult the problem is – you can rely on the precision and accuracy of our sig fig calculator. We designed the calculator in such a way that it is easy to use so the answer to your problem is just one click away!

## Examples of Signigicant Figures:

Use the following rules to determine the number of significant figures in a number:

Non-zero digits are always significant: All non-zero digits are considers as a significant figure. Whether the number place before decimal or after decimal is consider as a significant figure.

**For example:**

- 123.693 has 6 significant figures.
- 1.338 has 4 significant figures.
- 275.12 has 5 significant figures.

Any zeros between two significant digits are significant: If 0 appear in between two non-zero number is consider as a significant number. Whether 0 appear in between two non-zero number place before decimal or after decimal is consider as a significant figure.

**For example:**

- 1.2093 has five significant figures. In 1.2093 0 is between 2 non-zero digit and after the decimal. So it consider as a significant figure.
- 902.117 has six significant figures. In 902.117 0 is between 2 non-zero digit and before the decimal. So it consider as a significant figure.

Leading zeros: If 0 appear before decimal and after decimal are not consider as a significant figure. The 0 may be two or more than two, all are not consider as a significant.

**For example:**

- 0.00045 has 2 significant figure. The zero before and after decimal are not consider as a significant figure.
- 0000.0003 has 1 significant figure. The zero before and after decimal are not consider as a significant figure.

Trailing zeros: Trailing zero has 2 conditions.

The number without decimal: Trailing zero in a number without decimal is not consider as a significant.

**For example:**

- 567000 has 3 significant figures.
- 3427400 has 5 significant figures.

The number with decimal: Trailing zero in a number with decimal is consider as a significant.

**For example:**

- 96.700 has 5 significant figures.
- 54.87400 has 7 significant figures.