SWBAT determine orally & in writing what number set a value belongs to as well as provide example for each set.

Sonia measures her avg speed as 24mph due to traffic, how long will it take her to travel to and from Sprouts if it is 4.23 miles away? Please consider significant figures.

Solution:

24mph 2 sig figs4.23 miles 3 sig figs

D = r * t4.23 = 24 * t4.23/24 = t0.17625Round trip = 2 * tT = 0.3525 hr 0.35 hrs

Significant Figures Examples #1• 3.14159 has six significant digits (all the numbers give you useful

information)• 1000 has one significant digit (only the 1is interesting; you don't

know anything for sure about the hundreds, tens, or units places; the zeroes may just be placeholders; they may have rounded something off to get this value)

• 1000.0 has five significant digits (the ".0" tells us something interesting about the presumed accuracy of the measurement being made: that the measurement is accurate to the tenths place, but that there happen to be zero tenths)

• 0.00035 has two significant digits (only the 3 and 5 tell us something; the other zeroes are placeholders, only providing information about relative size)

Significant Figures Examples #2• 0.000350 has three significant digits (that last zero tells us that the

measurement was made accurate to that last digit, which just happened to have a value of zero)

• 1006 has four significant digits (the 1and 6 are interesting, and we have to count the zeroes, because they're between the two interesting numbers)

• 560 has two significant digits (the last zero is just a placeholder)• 560. (notice the "point" after the zero) has three significant digits (the

decimal point tells us that the measurement was made to the nearest unit, so the zero is not just a placeholder)

• 560.0 has four significant digits (the zero in the tenths place means that the measurement was made accurate to the tenths place, and that there just happen to be zero tenths; the 5 and 6 give useful information, and the other zero is between significant digits, and must therefore also be counted)

MS Quiz Zero!

• Timed 15 minutes.

• GO!

1.1 Number Sets

• Numbers are categorized into different groups

The different number sets are arranged in a hierarchy

Natural Numbers

• The most restrictive number set• Includes counting numbers• Starts with zero and then progresses

N ={0,1, 2, 3, 4, …}• Can be represented on a number line by

setting the origin (0) and a unit (what you are counting by)

Integers

Natural numbers and their negative counter parts.Must be whole numbersZ is {…,-4,-3,-2,-1,0,1,2,3,4, …}

Rational Numbers

• Q = { p/q where p and q are both integers}• Decimals that are finite or recurring digits• A number that can be represented by the

division of two integers aka basic Fractions• Q = {4, 2, 1, -4, -5/7, 0.666667}– Note that 0.666667 = 2/3

• The average of any pair of rational numbers is also a rational number

Real Numbers

• R = {Irrational, Rational, Integers, Natural}• Irrational numbers that can be represented as

non-terminating (never ending), non repeating (no magic hat) decimals– Includes Pi, e, and radicals that cannot be

simplified such as ,

True or False

1) A real number must be rational

2) An integer is always a rational number

3) An integer is always a real number

4) An integer is always a natural number

Homework:

• Investigation Natural Numbers pg 4• Investigation Integers pg 6• Investigation Rational numbers pg 9