Significant DigitsMeasurements

Description and Measurement

Key Vocabulary Precision Accuracy

Description and Measurement

Precision- how close measurements are to one another Example: If you

measure the width of a floor tile several times and you get: 1.0m, 1.1m, 1.0m, and 1.0m; then your results are precise

Description and Measurement

Accuracy- comparison of a measurement to an accepted value Example: when an archer shoots and arrow

and hits the bullseye, the archer is accurate

Description and Measurement

Description and Measurement

Significant Figures- you can only be as precise as your least precise measurement Digits other than zero (0) are always significant Zeros after a decimal point are significant Zeros between any other digit are significant Initial zeros are not significant Zeros at the end of a whole number may or may not

be significant Depends on if you place a decimal after the zero

Description and Measurements

How many significant figures in these examples 0.00678 seconds 1234.098 meters 350 kilometers 5.00 milliliters 450. grams

Description and Measurements

There are also rules to follow when deciding the number of significant digits in the answer to a calculation.

It depends on the type of calculation that you are doing.

Multiplying and Dividing with Significant Digits

The rule for multiplication and division is to look at the total number of significant digits in all of the numbers involved in the calculation. 

Then, decide what is the smallest number of significant figures you are working with in the problem. 

Example

1.35/17=

How many SD’s are in each number?

1.35?

17?

1.35- 3 Significant Digits

17- 2 Significant Digits

2 is the smallest number of SD’s, so our answer will have no more than 2 Significant Digits.

0.0794117 rounded to 2 SD’s= 0.079

Adding and Subtracting with Significant Digits

The # of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.

Example

5.67 J (two decimal places)

+

1.1 J (one decimal place)

+

0.9378 J (four decimal place)

7.7 J (one decimal place)

Quick Review

Would the sum of 5.7 and 6.2 need to be rounded? Why or why not?

Would the sum of 3.28 and 4.1 need to be rounded? Why or why not?

Quick Review

Solve these problems using the correct number of significant figures: 43.25 + 213= 61.2-3.95= 64.992-3.9= 7.5+6.71= 180 / 42.512= 59.515 / 40= 6.757 x 35.6= 6.3 x 20 x 30=