Pre Algebra (Period 2 & 4)

Decimal Review

First up: Place value

The root word in decimal is "decem" which means 10.

Each time you move in the decimal system you are multiplying or dividing the place value by 10.
If you move to the LEFT, place value is MULTIPLIED by 10. If you move to the RIGHT, place value is DIVIDED by 10 (or multiplied by 1/10...remember that dividing by 10 is the same as multiplying by its reciprocal...says our BFF, the Multiplicative Inverse Property)

The middle of the decimal system is the ones place (not the decimal!)

Place value names mirror each other to the left and to the right of the ones.
EXAMPLE: Take 1 and multiply by 10 and you get the TENS.

Take 1 and divide by 10 (or multiply by 1/10) and you get the TENTHS.

Another pattern in PLACE VALUE NAMES:

They are related to how many groups of "000" after 1,000
1 million = 1,000,000 

million is from "mille" which meant 1000 and 1 million is 1000 times 1000 or 1000¹ bigger than 1000
1 billion = 1,000,000,000 as in 1000 times 1000 times 1000 or 1000² bigger than 1000
One more example: 
1 trillion = 1,000,000,000,000 as in 1000³bigger than 1000

SO TO MAKE THIS EASIER TO UNDERSTAND:

EACH NEW PLACE VALUE NAME IS COUNTING THE GROUPS OF  ZEROS (000) AFTER 1000!

1 QUADrillion...QUAD means 4 so 4 groups of zeros after 1000:
1,000,000,000,000,000

AND OTHER THE OTHER SIDE OF THE DECIMAL, THE NAMES ARE THE SAME EXCEPT THEY HAVE A "TH"

What you need to do on the other side is to remember that the ones is still the starting point
on the left side of the decimal point though. So if you're looking for 1 millionth, you count 6
places in total = .000001
You see that there are only 5 zeros, not 6

1 millionth = 1 times 1/1,000,000 = .000001

Instead of writing all these zeros, we can use exponents.

Exponents for powers of 10 count the number of zeros.
So 1,000,000 = 106
and one millionth = 1/1,000,000 = 10-6

ROUNDING: 
Round 0 - 4 down and 5 - 9 up

EXAMPLE: 0.34 rounded to the tenths is 0.3
0.35 rounded to the tenths is 0.4
Notice you don't add zeros at the end
If there is a 9 in the next place, then think of rounding up as adding 1, that will make the number go up to "10"
EXAMPLE: 0.96 rounded to the tenths is 1.0

Think of it as adding 1 in the tenths column which would carry to the ones.
Now there is a zero in the tenths to show the reader of the number that you rounded to the tenths and not the ones.

EXAMPLE: 24,300 rounded to the thousands is 24,000

Now you need zeros to the decimal point or you'll lose the place value!

EXAMPLE: 29,600 rounded to the thousands is 30,000
Again, if it's a 9, it will need to go up to the next column...
Think of it as adding 1