Understanding the Concept- What Does Rounding to Three Significant Figures Mean-

What does round to 3 significant figures mean?

Rounding to three significant figures is a common practice in mathematics and science to simplify numerical values while retaining the most important information. Significant figures, also known as significant digits, are the digits in a number that carry meaning in terms of precision. When rounding to three significant figures, the goal is to keep three digits that are known with certainty and to discard or round the rest to make the number easier to work with or to fit within a specific format.

In a number, the first non-zero digit is always considered a significant figure. For example, in the number 12345, all five digits are significant. However, when rounding to three significant figures, we focus on the first three digits, which are 123. The fourth digit, 4, is the one that determines whether we round up or down. If the fourth digit is 5 or greater, we round up the third digit. If it is less than 5, we leave the third digit as it is.

Let’s consider a few examples to illustrate this concept:

1. Rounding 12345 to three significant figures:
The fourth digit is 4, which is less than 5. Therefore, we keep the first three digits, 123, and discard the rest.
Rounded number: 123

2. Rounding 12346 to three significant figures:
The fourth digit is 4, which is less than 5. Therefore, we keep the first three digits, 123, and discard the rest.
Rounded number: 123

3. Rounding 12347 to three significant figures:
The fourth digit is 4, which is less than 5. Therefore, we keep the first three digits, 123, and discard the rest.
Rounded number: 123

4. Rounding 12348 to three significant figures:
The fourth digit is 4, which is less than 5. Therefore, we keep the first three digits, 123, and discard the rest.
Rounded number: 123

5. Rounding 12349 to three significant figures:
The fourth digit is 4, which is less than 5. Therefore, we keep the first three digits, 123, and discard the rest.
Rounded number: 123

6. Rounding 12350 to three significant figures:
The fourth digit is 5, which is equal to 5. According to the rounding rule, we round up the third digit, which is 3, to 4.
Rounded number: 124

In summary, rounding to three significant figures involves keeping the first three digits of a number and rounding the fourth digit based on the rounding rule. This practice helps simplify numerical values while maintaining the most important information in a number.