MATH 10

Ms. Albarico

CHAPTER 1 DATA MANAGEMENT

1.2 Measuring

Ms. Albarico

Students are expected todetermine the accuracy and precision of

a measurement.

demonstrate an understanding of concerns and issues that pertain to the collection of data.

determine and apply formulas for perimeter, area, surface area, and volume.

Key Term:

Accuracy– the accuracy of a measurement indicates how close the recorded measurement is to the true value. It depends on the user’s skill in using the tool.

Accuracy and Precision

Key Term:

Precision – the precision of a measurement tool is the smallest unit that can be measured with confidence using the tool. It depends on the fineness of the scale on the tool.

SIGNIFICANT DIGITSSignificant digits are the numbers in a measurement.

For example, the number 26.3 has 3 significant digits. The first two numbers (26) are said to be certain, the third is uncertain (because somewhere it could have been rounded off).

Rules:1) All non zero digits are significant.Examples:517 51.7 5.17 -> 3 significant digits

2) For a decimal number, any zeros that appear after the last non-zero digit or between 2 non-zero digits are significant.

Examples:0.05057 5057 56.50 ->4 significant digits

3) For whole numbers, only zeros between two non-zero digits are significant.

Examples:47 470 4700 -> 2 significant digits

REMEMBER!All non-zero numbers are significant.Example: 143.257 has 6 significant digitsAll zeros between non-zero numbers are significant.Example: 3408 and 1.205 both have 4 significant digits All leading zeros are not significant. These zeros do

nothing but set the decimal place.Example: $1 000 000 has 1 significant digitAll trailing zeros after the decimal are significant.Example: 4.20 has three significant digitsAll trailing zeros before a decimal are significant only if

the decimal is present.Example: 100. has 3 significant digits

Notes:

When adding or subtracting, the right most digit in the result should be in the same position as that in the least precise measurement.

When multiplying or dividing, the number of significant digits in the result is the same as that of the measure of the least number of significant digits.

Adding and Subtracting – keep the same number of significant digits as the least number past the decimal. Remember that the last digit in each calculation is always uncertain, and our answer can only have one uncertain digit.

 one < two, therefore our answer will have one digit past the

decimal.

Ex. 11.2 + 17.34 = 28.5 one digit past the decimal two digits past the decimal  

SIGNIFICANT DIGITS

Multiplying and Dividing – keep the smallest number of significant digits.

 three < four, therefore our answer will have three significant digits in total.

Ex: 33.24 ÷ 2.59 = 12.8 Four significant digits in total

three significant digits in total       

SIGNIFICANT DIGITS

Class ActivityAnswer the practice exercise.

HOMEWORK:1) Finish the Investigation 1 at home.

Submit your assignment in A4 paper this Friday.

2) Don’t forget to bring a 40cm ruler for Investigation 2.