Fraction to decimal

We've been working on converting fractions into their decimal equivalents! We've been specifically looking at the meaning of place value and how to convert fractions with denominators of 10, 100, 1000, etc. into decimals using place value! The denominator determines where the numerator goes using place value...



Example 1:
1/100 = .01 the 1 is in the hundredths place (we have no tenths so the 0 "holds"
the 1 in the correct, hundredths place)

Example 2:
25/1000 = .025 the last digit in the numerator goes in the place value indicated by the denominator, which in this case is the thousandths place...then just back-fill until you get to the decimal. The decimal is read like a whole number but you then add the place value the last digit is in (twenty-five thousandths.....just like the fraction!)

Example 3:
101/100 = 1.01 (this is an improper fraction so we know that we have a value greater than 1 whole - not by very much in this case!)

example 4:
sometimes you have to create and equivalent fraction with a denominator of 10, 100, 1000, etc. before you can use our wonderful base-ten decimal system....if we had 4 fingered hands we've have a base-8 decimal system!!

4/25 = 16/100 (I multiplied the numerator and denominator both by 4)

16/100=0.16

Strategies for finding common denominators (also see video links for more help!)

Finding common denominators - Reasons:
(1) To accurately compare the relative value of 2 fractions (when denominator is same - same sized pieces- the one with the bigger numerator is larger...has more of these same sized pieces!) or
(2) to add & subtract fractions finding common denominators becomes essential because you need to be adding up (or subtracting) the same sized pieces or your answer won't make any sense!

Strategy/Example #1:

1/3 + 2/9 = _____
- Hmmm, well, since the denominator of the 1st fraction is a FACTOR of the second I should be able to use multiplication to create my common denom. because 3x3=9! Don't forget, to get an EQUIVALENT fraction (we don't want to add up a non-equivalent fraction, that would change the actual value of the problem!) we need to multiply the numerator and the denominator by the same #

1 x 3
__ = 3/9 and now we just substitute 3/9 into our original problem for 1/3
3 x 3


3/9 + 2/9 = 5/9 (remember, only add the denominators because that is how many pieces you
are adding - if you added the denominators you'd be changing the size of
your pieces which would, in effect, be making your sum of less value!)

Strategy/example #2:

1/5 + 2/4 = ____ well, neither denominator is a factor of the other so we have to find a
common multiple of both - easiest way to do this is to multiply 2
numbers together!! Here, like this:

1 x 4
___ = 4/20
5 x 4


2 x 5
__ = 10/20
4 x 5


Now, we can substitute our new, fancy equivalent fractions with common denominators in for the old ones and we get

4/20 + 10/20 = 14/20 which reduces to 7/10

Note: you can also use division to reduce fractions in order to find a common denominator - make sure you divide the numerator and the denominator by the same # and that the they are both divisible by that number!

Hello-
IPR's (interim progress report cards) are coming out this Thursday....meaning I have to submit my grades NO later than Wednesday. Soooooo, if you have any missing or late assignments to turn in this would be the weekend to get 'er done!

Science: Mass, Volume, and Density

Density, the measure of mass per unit volume, can be found by simply dividing the mass of an object by it's volume.
M/V=D

If you HAVE the density and volume and you want to figure out the MASS of an object, take your density and multiply it by your volume.
D x V = M

And if your looking for the VOLUME and you have the mass and density, just divide the mass by the density.

M/D = V

Remember, volume is the amount of SPACE something takes up, mass is a measure for how much matter is in an object and density is a measure of mass per volume. I also like to think of my garbage can after I forget to take out the garbage the previous week - the bin is the same size (volume) but I've been forced to increase the amount of matter (mass) in that same space thus increasing it's DENSITY!

oh, yeah...units we've been using in class:
* the gram(g) is a unit of MASS
* cubic centimeters (cm^3) or milliliters (mL) are units of VOLUME
* and grams per milliliter (g/mL) and grams per cubic centimeter (g/cm^3) is for DESNSITY