Measurement, Measurement, Estimation, Precision, & Estimation, Precision, & AccuracyAccuracy

How to make good How to make good measurements.measurements.

Chapter 2 section 1 in your Chapter 2 section 1 in your bookbook

MeasurementsMeasurementsMeasurements are used to describe the world with numbers.Each one of the devices shown below is used for measurement.

EstimationEstimationEstimation is a method of making a rough measurement of an object without having to actually measure it.Some sample estimations are given below.

These trees are about 2 meters apart.

This runner is about 25 years old.

PrecisionPrecisionPrecision is a description of how close measurements are together.

In this picture one arrow was split by another arrow. This shows a great deal of precision. It wouldn’t matter where the arrows were placed, if they were this close together there would be a high degree of precision.

AccuracyAccuracyAccuracy is a comparison of a measurement to the desired standard or true value.

These beakers can measure liquids, but not very accurately. If you were told to get 250 ml of a liquid this would not be an accurate way to do it. The markings on the side are not very accurate.

These flasks are a little more accurate than the beakers on the left. Notice how the markings on the side of the flasks are a little closer together providing a greater degree of accuracy.

These graduated cylinders would be the most accurate way to measure the liquid. They have markings on the side every 1 ml or less. This means you can be very accurate about your measurements.

Remember that for labs later this year. When measuring liquids you should always use a graduated cylinder if possible.

Rounding Rounding MeasurementsMeasurementsUnless you are told differently, all measurements in this

class will be rounded to 2 decimal places this year. If a measurement comes out as a whole number there is no need to put zeros after the decimal.

Rules for Rounding

1. Find the place value you are going to round to.

2. Look at the digit to the right of that place value.

3. If the digit is less than 5 then you leave the place value digit the same.

4. If the value is 5 or greater then you round the place value digit up to the next digit.

5. After rounding drop all of the digits to the right of the rounded place value.

Rounding ExamplesRounding ExamplesExample 1: Round 28.4553 to the nearest hundredth.

Find the digit in the place value you are rounding to.

28.4553Look at the digit to the right of the place value digit.

28.4553The digit is greater than 5, so round the place value digit up 1.

28.46__Drop the digits to the right of the place value digit.

28.46

Significant DigitsSignificant DigitsSignificant Digits refer to the number of digits in an answer that can be assumed to be accurate.Rules For Determining Significant Digits

Digits other than zero are always significant

Final zeros after a decimal point are significant

Zeros between any other digits are significant

Initial zeros are NOT significant.

Zeros in a whole number are generally not significant.

3.14159872563118

Calculating With Calculating With Significant DigitsSignificant Digits

When you are making calculations using significant digits you always use the number of the input with the least significant digits, or significant place value.Example 1: 38.42 X 3.7 = 142.154

Since 3.7 only has 2 significant digits, your answer can only have 2 significant digits. So your answer becomes 140

Example 2: 14.285 + 3.6 = 17.885

Since the tenths place value is the only one that is significant in both examples, that is as far as you can take your answer. Your answer becomes 17.9