SWBAT describe the difference between exact & approx. values using

rounding, significant figure, estimation and % error in writing by

completing a set of problems.Do Now: Solve and Graph these inequalities:1) 2) -2

Homework

Integer NumbersIntegers…

+ integer =- integer = X integer = integer =

Rational Numbers• Rational …

- rational = rational2 = = ration =

What’s the difference between an approximate and an exact value?

• What are some examples of approximate values?

• What are some ways we approximate?

Rounding• Approximating a number to a certain degree

or accuracy• How to Round:– Go to the digit after the one to which we are

rounding.– If it’s a 5 or more round up. – Less then 5 round down to zeros or– If decimal drop the zeros.

Rounding Lingo

• Rounding to the nearest ____ is the same as the rounding the nearest multiple of ____

Ex: Round to the nearest multiple of 100• Rounding to a number correct to ___ decimal

places is the same as rounding to the nearest blank.

Ex: Rounding a number correct to three decimals places is the same as the nearest thousandth

Rounding Practice

• Exerices 1H on page 15– #1-3, 5

Important Sig Fig Note!

• When doing multi-step calculations (as you usually do), use at least one more sig fig that is required at the end of the problem to maintain accuracy.

Ex: If the problem required 3 sig figs at the end, use four or more sig figs through out your calculation. Then round to 3 sig figs at the end.

Estimation

• An approximation usually used to check if an answer is reasonable and makes sense.

• Round all numbers in a calculation to 1 sig fig before completing the calculation.Ex: Jonny’s restaurant bill is 39.80 for him and his date tonight. He wants to impress her and leave over an 18% tip. How much should he leave?

Estimation Practice:

• Exercises 1K on pg 19-20 #1-7

Percentage Errors

• The difference between the estimated value and the exact value– In science it can be the difference between the

theoretical value and the experimental value“Hey, when I did the Millikan Oil Drop I calculated as 1.3 x 10-18 C. My percent error is going to be HUGE!!!”

Calculating the Error

• Take the difference between an estimate or approximate value and the exact value

Error = va – ve

Va = appoximate value

Ve = exact value

Percentage Error Formula

• % Error = x 100%

Phil calculated accelaration of gravity to be 9.54 m/s near the Earth’s surface. The accepted value is 9.81 m/s. What is the percent error?

Homework:

Pg 18 Ex 1JPg 21 Ex 1L