Why is a Leading Digit Not Counted As A Significant Figure If It is a 1?

Why is a Leading Digit Not Counted As A Significant Figure If It is a 1?

In positional notation, significant figures are the digits in a specific number that are used to represent the quantity of anything. Only the digits allowed by the measurement resolution are dependable. Therefore, only these can be significant figures if a number indicating the result of measurement of something (e.g., length, pressure, volume, or mass) includes more digits than the measurement resolution allows. An online sig figs calculator by calculator-online.net is exclusively designed to help people in figuring out the significant figures instantly. Is it not a good offer for you? Yes, it is!

Anyways, let us come to the point. In this technical content, we will be discussing the reasons why leading digits are not considered significant figures?

Also Read: In Time Zero, There was No Big-Bang

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Leading Digits in Significant Figures:

A leading significant number is actually a digit that has no value within the number. Any non-zero numbers or trapped zeros are significant figures. Leading and trailing zeros are not included in this category. What you need to keep in mind is that always maintain the same number of significant digits when switching from decimal to scientific notation. In case you find it difficult in doing so, try using the free sig figs calculator to perform swift calculations.

Example:

Suppose we have the digit 0.0025. In this number, only two digits are significant. But the leading zeroes are not supposed to fall in this category.

Why 1 is Not Considered a Significant Figure?

In physics, while writing significant figures, it is a better choice to round off them to a maximum of 3 individual digits. Here the online sig figs converter may display more than three digits, but a qualified engineer or physicist would always go selecting only three of them. 

Example:

As we all know that the gravity has a value to be \(9.98\frac{m}{s^{2}}\). Now if it was measured using sig figs calculator, you may get a large number containing a mixture of digits that could be significant and non-significant too. But the rule says that only three of them would be the resulting answer.

To clarify your idea in more depth, let us solve a numerical regarding it.

Determine the force that is required to provide an upward acceleration of \(9.98\frac{m}{s^{2}}\) to a 0.4kg heavy rocket.

Solution:

Here we know that:

$$ F = ma $$

$$ F – mg = ma $$

$$ F – 0.4 * 9.81 = 0.4 * 40 $$

$$ F = 19.92N $$

The free sig figs calculator may result in 19.92 which is also correct. But as the value of acceleration is 9.8, we will simply ignore the leading 1 to get the answer as below:

$$ F = 9.92N $$

Rules to Write Significant Figures:

The basic criteria for identifying the significant figures are that you must know how to figure out reliable numbers. But in case you do not have any idea about it, do not just panic. The online sig figs calculator would be doing that for you in no time and accurately. But when it comes to manual calculations, you may face a problem. But we have arranged the proper content below to help you in writing the significant figures without any hurdle. Let us and how to do that!

Rule # 01:

The presence of non-zero digits inside a measurement or reporting resolution is significant.

For example:

The number 251 has three significant figures if they are included in the measurement resolution. Similarly, the number 235.214 has six significant figures.

Rule # 02:

If there is a zero in between two non-zero significant digits, then it is considered a significant digit.

For example:

1.203 has four significant figures. Likewise, the number 1002.320124001 has thirteen significant figures. The online significant figures calculator also depicts the same results and in no time.

Rule # 03:

The zeroes that are present to the left of the non-zero digit are considered non-significant figures.

For example:

If the measure of a length gives you a number of 0.021km, then it would be equal to 21m. This shows that you have only two significant figures say 2 and 1. In the same way, 0.00032 has four significant figures if the resolution is taken as 0.001(the numbers 3 and 4 are beyond the resolution and are not considered as significant figures).

Rule # 04:

In a number with a decimal point, the zeros to the right of the final non-zero digit are significant which can also be determined using the sig figs calculator.

For example:

If the measurement resolution allows it, 1.600 contains four significant figures (1, 6, 0, and 0).

Rule # 05:

In an integer, the trailing zeros may or may not be important.

For example:

Depending on how the last zeros are used, 45,600 have significant figures as 4, 5, and 6.

Rule # 06:

The number of the significant figures in an exact number is supposed to be infinite.

For example:

Suppose Jack has 5 oranges in a bag, which is an exact number. Then we can simply say that the number 5 can be written as 5.0000… which means the trailing zeroes to the right just after the decimal point are significant.

Rule # 07:

The known digits of a mathematical or physical constant have significant figures.

For example:

π is an irrational number that shows a ratio of the circumference of the circle to its diameter. Its value is 3.1415926535… but in case you carry out computations using this number, only finite digits are supposed to be considered. Remember that all the digits in the π are significant figures. Our free significant digits calculator also goes with the same phenomenon and verifies it.

Wrapping It Up:

Significant figures are used in scientific and mathematical computations to ensure that numbers are accurate and precise. It’s crucial to evaluate the final result’s uncertainty, and this is where significant figures come in handy. 

In this guidepost, we had detailed content about writing significant figures and considering leading 0 and 1 as non-significant. Also, the use of the free online sig figs calculator has also been highlighted in the reading for maintaining a better precision in the calculations. We hope it will help you a lot!

Good Luck!

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