Which of the measurements contain four significant figures is a common question in scientific and mathematical contexts. Significant figures, also known as significant digits, are the digits in a number that carry meaning in terms of precision. Understanding how to identify and count significant figures is crucial for accurate calculations and data representation. In this article, we will explore various examples and guidelines to help you determine which measurements contain four significant figures.
The first step in identifying significant figures is to understand their rules. Here are some key rules to follow:
1. All non-zero digits are significant. For example, in the number 123, all three digits are significant.
2. Leading zeros (zeros at the beginning of a number) are not significant. For instance, in 0.0023, only the digits 2, 3, and the trailing zero are significant.
3. Trailing zeros are significant if they are after a decimal point. In 1.230, all four digits are significant. However, in 1200, only the digits 1 and 2 are significant, as the trailing zeros are placeholders.
4. Zeros between non-zero digits are always significant. For example, in 1001, all four digits are significant.
Now, let’s apply these rules to some examples to determine which measurements contain four significant figures:
1. 0.00450: In this number, the leading zeros are not significant, and the trailing zero after the decimal point is significant. Therefore, this measurement contains four significant figures.
2. 2.345: All digits in this number are non-zero, making it a total of four significant figures.
3. 1200: As mentioned earlier, the trailing zeros are not significant in this case. Hence, this measurement contains only two significant figures.
4. 1.230: This number has four significant figures, as all digits are non-zero and the trailing zero after the decimal point is significant.
In conclusion, identifying which measurements contain four significant figures requires applying the rules of significant figures. By understanding these rules and practicing with various examples, you can ensure accurate calculations and data representation in scientific and mathematical contexts.
