Significant Figures

Significant figures are the digits that are important when we measure something. They include digits from 1 to 9, and sometimes 0, depending on their position in the number. Scientists and engineers use significant figures to measure things like length, volume, and mass accurately. For example, 579 has three significant figures: 5, 7, and 9.

The two main reasons we use significant figures are precision and accuracy. 

Precision: Getting the same result while measuring something multiple times under the same conditions is called precision. If you and your friend measure a pen’s length and both get close to 10 cm each time, that means your measurements are precise.

Accuracy: Accuracy means how close your answer is to the correct value. If the water bottle’s volume is 1.5 liters, and you measure it as 1.47 liters, then your measurement is accurate because it is close to the correct volume.

Significant figures are the digits that show how exact the measurement is. Follow the steps given below to identify them.

Step 1: Start counting from the first non-zero digit.
Ignore the zeros at the beginning; you have to start counting from the first non-zero number.

Step 2: Count all the numbers from the first non-zero digit.
Start counting from the first non-zero digit, including all the non-zero and zeros in the given number.

Step 3: Add the decimal zeros at the end
If there is a decimal point, count the zeros that come only after the decimal; don’t count the zeros that are at the start of the given number. 

Step 4: Significant numbers
The number of digits you counted in the above steps gives the total number of significant figures.

Let's look at an example for finding the significant figures.
For example, in 0045, the first non-zero digit is 4. So count 4 and 5. Therefore, the given number has 2 significant figures.

There are certain simple rules to help us count significant figures. Below are some simple rules.

Rule 1: All non-zero numbers are significant

The numbers that are not zero can be counted as significant figures. If the number is 125, all three digits are non-zero; therefore, it has 3 significant figures.

Rule 2: Zeros between non-zero numbers are significant

The zero that lies between two non-zero numbers is considered a significant number. For example, in 5006 we count the zeros because the zeros are between two non-zero digits, it is counted. So, the number has 4 significant figures.

Rule 3: Zeros before the first non-zero digit are not significant

If a zero comes before the first non-zero digit, it cannot be considered a significant figure. In the number 00087, the first non-zero digit is 8; the zeros before 8 are not counted. Therefore, the number has 2 significant digits.

Rule 4: Zeros at the end of the decimal are significant

The zeros that are after the decimal point and are at the end of a number can be counted as significant digits. The number 3.50 has 3 significant figures because the zero lies at the end of the number after a decimal point, so the zero is counted as a significant figure.

Rule 5: Zeros at the end of the number without a decimal point are not significant

The zeros at the end of the given number without a decimal point cannot be counted as a significant figure. In the number 4200, there are zeros at the end, but there is no decimal point; therefore, the zeros are not counted. So the number 4200 has only 2 significant figures.

Rounding off significant figures means shortening a number by removing some digits. Here are the steps to round off the significant figures.

Step 1: Look at the number you want to round.

Step 2: Find the digit right of the last significant figure you want to keep.

Step 3: If the digit is less than 5, keep the number the same. If the digit is more than 5, increase the last digit by 1 and remove the rest.

Step 4: Always consider the number as a whole when rounding to significant figures

Example: Round the number 2748 to 3 significant figures.

1. The first three significant figures are 2, 7, and 4.

2. The next digit is 8, which is greater than 5, so we need to round up.

3. Therefore, the number becomes 2750.

Significant figures are useful in many fields where accuracy and precision are needed. Here are some key areas where they are used.

Medicine & Healthcare

Doctors and pharmacists need to be very exact when giving medicine. Significant figures help make sure the patient gets the right amount. This helps avoid giving too much or too little medicine.

Banking & Finance

Banks use significant figures to calculate interest, loans, and currency exchange. It helps them make correct payments and avoid money mistakes that could lead to loss.

Science & Research

Scientists use significant figures when they measure things like chemicals, temperature, or distances. This helps make their results correct and avoids wrong answers in their research.