Significant Figures Calculator | Sig Fig Calc

Meet the “Significant Figures Calculator” aka the “Sig Fig Calc”! This thing will do calculations for you with precision. Whether you’re a student doing science experiments, a physicist or chemist, or anyone who needs numbers, we’ve got you covered. Rounding numbers to significant figures and step by step calculations have never been easier.

Significant Figures Calculator

Enter number or expression (e.g., “5.13*3.78-4+4.6”):

Calculate

Results

Decimal notation:

No. of significant figures:

No. of decimals:

Scientific notation:

E notation:

Calculation Steps

Also Use: "Calculate GPA For UAE" | "PPP index tool" | "Scientific calculations Helper".

Sig Figs

Sig figs are a math and science concept. They are used to convey the precision and accuracy of numbers. Sig figs are all the numbers in a value that matter. To avoid clutter and redundancy non sig figs are often rounded but you must be careful not to lose precision in the process. A rounding calculator can be helpful in those cases.

Rules for Significant Figures

To determine which numbers in a number are significant and which are not we follow these rules:

1. Zeros to the left of a decimal point less than 1 are not significant.
2. Trailing zeros are not significant.
3. Zeros between non zero numbers are significant.
4. All non zero numbers are significant.

If a number has more digits than the number of significant figures required it must be rounded. For example 987,600 is rounded to 988,000 when expressed to 5 significant figures using the standard "half up" rounding. Zeros at the end of a number may not be significant but are retained as removing them would change the value unless the number is in scientific notation.

Using the Sig Fig Calculator

Now that we know the rules for significant figures let’s use this sig fig calculator.

Significant Figures in Math

When doing math operations like addition, subtraction, multiplication and division there are specific rules:

• Addition and Subtraction: The result should have no more decimal places than the number in the operation with the least number of decimal places. For example in 87.321 + 1.457 + 0.003 the number with the least number of decimal places is 0.003. So the result should also have 3 decimal places: 87.321 + 1.457 + 0.003 = 88.781.
• Multiplication and Division: The result should not have more significant figures than the number with the least significant figures. For example in 6.235 × 2.4 the number with the least significant figures (2) is 2.4. So the result should be 2 significant figures: 6.235 × 2.4 = 15.

Significant Figures Rules in Different Operations

In the world of mathematics and science, different operations call for different rules when it comes to significant figures. Here's a breakdown:

Operation	Rule	Examples
Addition	Use the fewest number of decimal places specified in any of the operands.	2.46 + 6.1743 = 8.63
Subtraction	Use the fewest number of decimal places specified in any of the operands.	3.1415 - 2.2 = 0.9
Multiplication	Use the fewest number of significant figures specified in any of the operands.	1530 × 4.0 = 6100<br>1530 × 4 = 6000
Division	Use the fewest number of significant figures specified in any of the operands.	444 ÷ 4 = 100<br>444 ÷ 111 = 4.00
Exponentiation	Use the same number of significant figures as the base.	210 = 1e3<br>2.00010 = 1024
Logarithms	Use the same number of decimal places in the result as the number of significant figures in the number you're taking the logarithm of.	log10(27) = 1.43<br>ln(0.026) = -3.65
Antilogarithms	Use the same number of significant figures in the result as the number of decimal places in the number you're taking the antilogarithm of.	103.43 = 2700<br>e-3.65 = 0.026

These rules help ensure precision and consistency in calculations across various mathematical and scientific contexts. Understanding them is vital for accurate and meaningful results in your academic journey.

Exact Values and Their Role

Exact values, including defined numbers like conversion factors and pure numbers, do not impact the precision of calculations. They can be treated as having an infinite number of significant figures. For example, when converting speed from m/s to km/h, you multiply the value in m/s by 3.6. The number of significant figures is still determined by the accuracy of the initial speed value in m/s. For instance, 25.6 m/s × 3.6 = 92.16 km/h.

Understanding and applying significant figures is essential for achieving accurate and meaningful results in scientific and mathematical endeavours.

FAQ: Sig Fig

Q1: How many sig figs in 100?

100 has one sig fig (and it’s the 1). Why? Trailing zeros don’t count as sig figs when there’s no decimal point.

Q2: How many sig figs in 100.00?

100.00 has five sig figs. This is because trailing zeros do count as sig figs when there’s a decimal point.

Q3: How many sig figs in 0.01?

0.01 has one sig fig (and it’s the 1). Why? Leading zeros don’t count as sig figs.

Q4: How many sig figs in 0.00208 grams?

0.00208 has three sig figs (2, 0, and 8). Why? Leading zeros don’t count as sig figs, but zeroes in the middle do.

Resource: Sig fig data from Wikipedia "here".