Topic: Types of Numbers and Number Sense

Purpose:(a) To understand the many different types of numbers. (b) To develop your “number sense” so you can understand and communicate better.

Question:(a) What is your “strategy” for communicating clearly with numbers?

Rational NumbersNatural: 1,2,3,4,5….

Whole: 0 + Natural0,1,2,3,4,5….

Integers: Negative and Positive Whole Numbers …-4,-3,-2,-1,0,1,2,3,4…

Rational: Natural, Whole, Integers Fractions and Decimals

Irrational NumbersIrrational:

(a) It is a “never ending” decimal

EX/ 2.3936773519097432….on and on

(a) Can not be written as a “fraction” EX/ = 1.414213….never ending

this can not be put into a fraction

What are all numbers called???

Real Numbers!….Real Numbers!!…Real Numbers!!!…Real Numbers!!!!

***including ALL rational and irrational numbers***

Don’t forget the Question we are responsible to know by the end of our lesson?!?

So what is the difference between the following?

1) ½ 2) 0.5 3) 50% 4) 2:4 5) 50/100

a) ratio b) rate c) percentage d) fraction e) proportion

The answer is : They are all the _________________!!!

Or wait….maybe there is a difference?

Question:(a) What is your “strategy” for communicating clearly with numbers?

Significant FiguresComing from the left, the first non-zero digit is the first significant figure and then count all the numbers going towards the right as significant figures as well

Ex. 310.45 start counting from 3 until the 5 5 significant figures0.003250 start counting from 3 until the 0 4 significant figures1.324028 start counting from 1 until the 8 7 significant figures

To read and write decimals, use the following steps:

Step #1: First, read the digits to the left of the decimal point as a whole number.

Step #2: Say and for the decimal point.

Step #3: Read the digits to the right of the decimal point as a whole number

Step #4: Say the place name of the last digit.

Examples:

25.578 is read twenty five and five hundred seventy eight thousandths

7000.14 is read seven thousand and fourteen hundredths

0.002 is read two thousandths

Notice that there is no need to say zero and two thousandths.

250.00035 is read two hundred fifty and thirty five hundred-thousandths

Significant Figures: How to read a decimal!!!

Scientific Notation and Decimals

1: Take a three digit numbers. (eg: 123) 2: Now reverse the digits. (reverse of 123 is 321) 3: Now, subtract smaller number from bigger number. (in our case 321-123=198) 4. Now reverse the digits in step 3. (ie 198 becomes 891) 5. Now, add 891 and 198. 6. The answer is _______________

Age Calculation Tricks:Step1: Multiply the first number of the age by 5. (If <10, ex 5, consider it as 05. If it is >100, ex: 102, then take 10 as the first digit, 2 as the second one.)Step2: Add 3 to the result.Step3: Double the answer.Step4: Add the second digit of the number with the result.Step5: Subtract 6 from it.

Trick 1: 2's trickStep1: Think of a number .Step2: Multiply it by 3.Step3: Add 6 with the getting result.Step4: divide it by 3.Step5: Subtract it from the first number used.