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 quantities such as 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: Precision is achieving the same result when measuring something multiple times under identical conditions. 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 refers to how close a measurement is to the true or accepted 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 digits that indicate the precision of a measurement. Follow the steps given below to identify them.

Step 1: Start counting from the first non-zero digit.

Ignore leading zeros and start counting from the first non-zero digit.

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 the number has a decimal point, count only the zeros after the decimal; leading zeros are not counted.

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

Zeros between non-zero digits are considered significant figures. 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

Trailing zeros after a decimal point are counted as significant figures. 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

Trailing zeros in a whole number without a decimal point are not significant. 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 significant figures involves shortening a number by adjusting its digits appropriately. 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, leave the last significant figure unchanged. If it is 5 or greater, increase the last significant figure by 1.

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 essential in fields requiring precise and accurate measurements. Here are some key areas where they are used.

Medicine & Healthcare

Doctors and pharmacists need to be very exact when giving medicine. Significant figures ensure that patients receive the correct dosage. This helps avoid giving too much or too little medicine.

Banking & Finance

Banks use significant figures to calculate interest, loans, and currency exchange. They help ensure accurate transactions and prevent financial errors. 

Science & Research

Scientists use significant figures when they measure things like chemicals, temperature, or distances. This ensures accurate results and prevents errors in research outcomes.