Place Value Chart

The value of each digit depends on its position or "place". Understanding place value is an important skill. In the example below, the 7 represents both ten thousands and also the millionths places. The digits are the same but the value of each is different due to their placement within the number.

The real trick to correctly read a number lies in your ability to read three digit numbers and recognizing the period of that three-digit number. For example the number below is read:

"3 trillion, 692 billion, 581million, 470 thousand, 369 and 2 million, 581 thousand, 470 ten-millionths"

There are three things to note. First, the word and is said only at the decimal point. It is used to indicate the change from the whole number part and the decimal number part.

Second, students of math often mistakenly believe in the existence of a "oneths" place. It is good to note that each decimal number is nothing more than a fraction with a denominator that is a power of ten, (ten, one hundred, thousands, ten thousands, hundred thousands, etc).

The third and perhaps the more challenging-skill to note is that the decimal part is not separated by commas into periods. When reading the decimal number, you must read the decimal part as though it was a whole number then state the name of the last (right-most) place. 3 , 6 9 2 , 5 8 1 , 4 7 0 , 3 6 9 . 2 5 8 1 4 7 0 Chapter 1 Notes

This is where we get the concept of the “Powers of Ten”

10 0 = 1 one

10 1 = 10 x 1 = 10 = 1 group of ten = 10 ones

10 2 = 10 x 10 = 100 = 1 group of a hundred = 10 tens

10 3 = 10 x 10 x 10 = 1,000 = 1 group of a thousand = 10 hundreds

10 4 = 10 x 10 x 10 x 10 = 10,000 = 1 group of ten thousands = 10 thousands

10 5 = 10 x 10 x 10 x 10 x 10 = 100,000 = 1 group of a hundred thousands = 10 ten thousands

10 6 = 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 = 1 group of a million = 10 hundred thousands

(It can keep building into infinity.)

Expanded Form looks like: 456,132 = 400,000 + 50,000 + 6,000 + 100 + 30 +2

Scientific Notation should look like this: 3 x 103 = 3,000

Greater Than > Less Than

Bigger Number > Smaller Number

inverse means opposite or reverse operation- what you do to solve a problem or answer a question ( + - x ÷)

We use inverse operations to check our work. Addition is the inverse of subtraction and multiplication is the inverse of division.

Example:

1 + 2 = 3 and 3-2 = 1 3 x 2 = 6 and 6 ÷ 2 = 3