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The significant figures calculator converts any number into a new number with the desired amount of sig figs AND solves expressions with sig figs (try doing 3.14 / 7.58 - 3.15). What are the significant figures rules? Those concepts will be explained throughout this page as well as how to use a sig fig calculator.

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Significant figures are all numbers that add to the meaning of the overall value of the number. To prevent repeating figures that aren't significant, numbers are often rounded. One must be careful not to lose precision when rounding. Many times the goal of rounding numbers is just to simplify them. Use the rounding calculator to assist with such problems.

To determine what numbers are significant and which aren't, use the following rules:

1. The zero to the left of a decimal value less than 1 is not significant.

2. All trailing zeros that are placeholders are not significant.

3. Zeros between non-zero numbers are significant.

4. All non-zero numbers are significant.

5. If a number has more numbers than the desired number of significant digits, the number is rounded. For example, 432,500 is 433,000 to 3 significant digits (using half up (regular) rounding).

6. Zeros at the end of numbers that are not significant but are not removed, as removing them would affect the value of the number. In the above example, we cannot remove 000 in 433,000 unless changing the number into scientific notation.

Our significant figures calculator works in two modes - it performs arithmetic operations on multiple numbers (for example, 4.18 / 2.33) or simply rounds a number to your desired number of sig figs.

Following the rules noted above, we can calculate sig figs by hand or by using the significant figures counter. Suppose we have the number 0.004562 and want 2 significant figures. The trailing zeros are placeholders, so we do not count them. Next, we round 4562 to 2 digits, leaving us with 0.0046.

Now we'll consider an example that is not a decimal. Suppose we want 3,453,528 to 4 significant figures. We simply round the entire number to the nearest thousand, giving us 3,454,000.

What if a number is in scientific notation? In such cases, the same rules apply. To enter scientific notation into the sig fig calculator, use E notation, which replaces × 10 with either a lower or upper case letter 'e'. For example, the number 5.033 x 10²³ is equivalent to 5.033E23 (or 5.033e23). For a very small number such as 6.674 x 10⁻¹¹ the E notation representation is 6.674E-11 (or 6.674e-11). You can read more about this convention in the scientific notation calculator.

When dealing with estimation, the number of significant digits should be no more than the log base 10 of the sample size and rounding to the nearest integer. For example, if the sample size is 150, the log of 150 is approximately 2.18, so we use 2 significant figures.

There are additional rules regarding the operations - addition, subtraction, multiplication, and division.

For addition and subtraction operations, the result should have no more decimal places than the number in the operation with the least precision. For example, when performing the operation 128.1 + 1.72 + 0.457, the value with the least number of decimal places (1) is 128.1. Hence, the result must have one decimal place as well: 128.̲1 + 1.7̲2 + 0.45̲7 = 130.̲277 = 130.̲3. The position of the last significant number is indicated by underlining it.

For multiplication and division operations, the result should have no more significant figures than the number in the operation with the least number of significant figures. For example, when performing the operation 4.321 × 3.14, the value with the least significant figures (3) is 3.14. So the result must also be given to three significant figures: 4.32̲1 × 3.1̲4 = 13.̲56974 = 13.̲6.

If performing addition and subtraction only, it is sufficient to do all calculations at once and apply the significant figures rules to the final result.

If performing multiplication and division only, it is sufficient to do all calculations at once and apply the significant figures rules to the final result.

If, however, you do mixed calculations - addition/subtraction and multiplication/division - you need to note the number of significant figures for each step of the calculation. For example, for the calculation 12.1̲3 + 1.7̲2 × 3.̲4, after the first step, you will obtain the following result: 12.1̲3 + 5.̲848. Now, note that the result of the multiplication operation is accurate to 2 significant figures and, more importantly, one decimal place. You shouldn't round the intermediate result and only apply the significant digit rules to the final result. So for this example, the final steps of the calculation are 12.1̲3 + 5.̲848 = 17.̲978 = 18.̲0.

Exact values, including defined numbers such as conversion factors and 'pure' numbers, don't affect the accuracy of the calculation. They can be treated as if they had an infinite number of significant figures. For example, when using the speed conversion, you need to multiply the value in m/s by 3.6 if you want to obtain the value in km/h. The number of significant figures is still determined by the accuracy of the initial speed value in m/s - for example, 15.23 × 3.6 = 54.83. Y

To use an exact value in the calculator, give the value to the greatest number of significant figures in the calculation. So for this example, you would enter 15.23 × 3.600 into the calculator.

Since we are talking about basic arithmetic operations, how about checking our distributive property calculator to learn how to handle complex mathematical problems that involve more than one arithmetic operation?

100 has one significant figure (and it's a number 1). Why? Because trailing zeros do not count as sig figs if there's no decimal point.

100.00 has five significant figures. This is because trailing zeros do count as sig figs if the decimal point is present.

0.01 has one significant figure (and it's a number 1). Why? Because leading zeros do not count as sig figs.

0.00208 has three significant figures (2, 0, and 8). Why? Because leading zeros do not count as sig figs, but zeroes sandwiched between non-zero figures do count.

100.10 has five significant figures, that is, all its figures are significant. Why? Because the zeroes sandwiched between non-zero figures always count as sig figs, and there is the decimal dot, so the trailing zeros count as well.

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Significant Figures Calculator - Sig Fig

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The significant figures calculator converts any number into a new number with the desired amount of sig figs AND solves expressions with sig figs (try doing 3.14 / 7.58 - 3.15). What are the significant figures rules? Those concepts will be explained throughout this page as well as how to use a sig fig calculator.

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Overview

This kinesthetic activity helps students grasp the difficult concept of significant figures. Student groups compete with each other to generate answers to questions about significant figures (also called significant digits). Each student holds a card with a single digit (0 to 9), decimal, or negative sign. Students organize themselves so that their cards show the correct answers.

Content standards

This activity is appropriate for middle and high school students and addresses the following National Science Education Standard:

Grades K-12, Unifying Concepts and Processes: Constancy, Change, and Measurement

Background

Measurement values are only as accurate as the measurement equipment used to collect them. For example, measuring meters with a meter stick is rather accurate; measuring millimeters (1/1,000 of a meter) with a meter stick is inaccurate. Using significant figures helps prevent the reporting of measured values that the measurement equipment is not capable of determining. A significant figure is comprised of the fewest digits capable of expressing a measured value without losing accuracy. As the sensitivity of the measurement equipment increases, so does the number of significant figures. Knowing the rules for working with significant figures can help your students. "Rounding" numbers is the usual method of achieving significant figures. Once the appropriate number of significant figures for any measurement, calculation, or equation is determined, students can practice rounding their answers appropriately.

Rules governing significant figures

Basic rules

1. Any non-zero digit is significant.

2. Zeros between non-zero digits are always significant.
Example: 3,606 has 4 significant figures.

3. Zeros that indicate the decimal point are not significant.
Example: 360,600 has 4 significant figures.

4. Zeros following a decimal are significant.
Example: 3.60 has 3 significant figures but 3.6 has 2.

5. Zeros appearing before a non-zero digit are not significant.
Example: 0.009 only has 1 significant figure.

Addition and subtraction rule

The number of significant figures in a sum or difference is equal to that of the least accurate measurement in the equation. The answer must contain the same number of decimal places as the least accurate measurement.
Example: Without using significant figures: 606.02 - 65.3 = 540.72
Using significant figures: 540.7

Multiplication and division rule

The number of significant figures in a product or quotient is equal to that of the least accurate measurement in the equation. The answer must contain the same number of significant figures as the least accurate measurement.
Example: Without using significant figures: 606.02 × 63 = 38,179.26
Using significant figures: 38,000 (has only 2 significant figures)

Materials

Blank Paper or Card Stock (11 for each group)

Thick Marking Pen

Calculators (optional)

Measuring Equipment (to use as examples)

Pre-activity (teacher)

Determine the number of groups in your class.

Assemble 11 sheets of paper or card stock to make up a set for each group.

On each sheet of paper in a set, write 1 value (0 to 9), a decimal point, or a negative sign.

Procedure (teacher)

1. Provide an overview of significant figures. Review the significant figure rules presented in the background section. Display examples of measuring equipment with variations of sensitivity.

2. Organize student groups and distribute 1 set of numbers to each group.

3. Facilitate or assign a student to facilitate each level of the games.

4. Award points for correct answers.

5. Have fun with the Significant Figure Race.

Significant figure race

Level 1

1. The facilitator asks basic significant figure questions.

2. Students race to get in place and hold up cards that form the correct answers.
Example questions:

1. How many significant figures are in 1,500?
Answer: 2

2. How many significant figures are in 1,500.01?
Answer: 6

3. How many decimal places are in 2.234?
Answer: 3 (This concept is useful for addition and subtraction questions later in this activity.)

Level 2

1. The facilitator asks addition or subtraction questions.
Example questions:

1. Which number is less accurate: 301 or 3.01?
Answer: 301

2. What is 60 + 83.2, using significant figures?
Answer: 143

3. What is 0.158 + 0.4, using significant figures?
Answer: 0.6

4. What is 0.11 - 2.2, using significant figures?
Answer: -2.1

Level 3

1. The facilitator asks multiplication or division questions.
Example questions:

1. What is 63.4 × 151, using significant figures?
Answer: 95,700

2. What is 610 ÷ 9.1, using significant figures?
Answer: 67

Level 4

1. The facilitator gives parameters for a number and the students race to build it.

2. After the students build their numbers, the adjacent group checks their results.
Example questions:

1. Give a number between -1 and 1 that has 5 significant figures.

2. Give a number greater than 1,000 that has 2 decimal places.

3. Give a number that is 4 digits but only has 3 significant figures.

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This kinesthetic activity helps students grasp the difficult concept of significant figures. Student groups compete with each other to generate answers to questions about significant figures (also called significant digits). Each student holds a card with a single digit (0 to 9), decimal, or negative sign.

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Can you name the number of significant digits in each number? Test your knowledge on this science quiz to see how you do and compare your score to others. Quiz by starwars314159

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SUGGEST HOW TO WRITE THIS NUMBER USING SCIENTIFIC NOTATION: 8980.34

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This quiz is designed to test your reading comprehension and understanding of the Scientific Notation section of the Online Study Guide to Chemistry.

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Hind salem 9/54 group the dodo

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Latifa ateeq , wadima saeed , ousha

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Shams and mozoun

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Salama m , amna , fatima obaid

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Group dodo(hamda)

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Note: each of the QR codes is a text file. There is no need for the mobile devices to connect to the internet to decode them.