Physics » The Nature of Physics » Approximation

# Summary and Main Ideas

## Summary of lessons so far

The following are the main ideas from the lessons so far:

• Accuracy of a measured value refers to how close a measurement is to the correct value. The uncertainty in a measurement is an estimate of the amount by which the measurement result may differ from this value.
• Precision of measured values refers to how close the agreement is between repeated measurements.
• The precision of a measuring tool is related to the size of its measurement increments. The smaller the measurement increment, the more precise the tool.
• Significant figures express the precision of a measuring tool.
• When multiplying or dividing measured values, the final answer can contain only as many significant figures as the least precise value.
• When adding or subtracting measured values, the final answer cannot contain more decimal places than the least precise value.
• Scientists often approximate the values of quantities to perform calculations and analyze systems.

## Glossary of Words

### Accuracy

the degree to which a measured value agrees with correct value for that measurement

### Approximation

an estimated value based on prior experience and reasoning

the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation

### Percent uncertainty

the ratio of the uncertainty of a measurement to the measured value, expressed as a percentage

### Precision

the degree to which repeated measurements agree with each other

### Significant figures

express the precision of a measuring tool used to measure a value

### Uncertainty

a quantitative measure of how much your measured values deviate from a standard or expected value