How many significant figures are there in each of the following values? (c) 75.0

Verified step by step guidance

1. Identify all the digits in the number. In this case, the number is 75.0.
2. Determine which digits are significant. All non-zero digits are always significant. Here, '7' and '5' are non-zero and thus significant.
3. Check if there are any trailing zeros after a decimal point. Trailing zeros after a decimal point are significant. In this case, the '0' after the decimal point is significant.
4. Count all the significant digits. Here, you have '7', '5', and '0' after the decimal point, making a total of three significant figures.
5. Conclude that the number 75.0 has three significant figures.

Key Concepts

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for accurately reporting measurements and calculations in scientific contexts.

Rules for Counting Significant Figures

There are specific rules for determining the number of significant figures in a value. Non-zero digits are always significant, leading zeros are not significant, and trailing zeros in a decimal number are significant. For example, in the number 75.0, the '7' and '5' are significant, and the trailing '0' is also significant due to the decimal point.

Precision vs. Accuracy

Precision refers to the consistency of repeated measurements, while accuracy indicates how close a measurement is to the true value. Significant figures help convey the precision of a measurement. In the case of 75.0, the presence of the decimal point and the trailing zero indicates a precise measurement, suggesting that the value is known to one decimal place.