Scientific Notation
Expressing Numbers as Powers of Ten
(1) Study the whole number area of the place value chart to the left of the decimal point. Note the NAME of the section (ex. Thousand); the value of each place (1, 10, 100); the prefix that represents the SECTION (ex. kilo-); and the abbreviation or symbol (ex. k).
(2) Study the fractions section of the place value chart to the right of the decimal point. Notice the section NAME (ex. tenths), the fraction (1/10); the prefix (deci-); and the abbreviation or symbol (ex. d).
(3) Study Table 5, the SI (International Standard) Number Chart that shows the FACTOR, the prefix, and the symbol for the major place value sections.
(4) Note the FACTOR or Scientific Notation for each number. It is a short way to express a number without writing out all of the zeros!
HOW SCIENTIFIC NOTATION WORKS:
1 is the base unit.
1 is 1-digit. 1 is followed by 0 zeros, so in Scientific Notation, 1 is written as 10
10 is a 1 followed by 1 zero, so 10, in Scientific Notation, is written as 101
100 is a 1 followed by 2 zeros, so 100, in Scientific Notation, is written as 102
Each time you MULTIPLY 1 by 10, you add a 0 to the UNIT 1: 1 x 10 = 10
10 x 10 = 100
100 x 10 = 1000 ...
Each 10 that is the MULTIPLIER is a FACTOR and the result is the PRODUCT.
This is why Scientific Notation, NOTES FACTORS of 10 or MULTIPLES of 10.
1,000 is a 1 followed by 3 zeros, so 1,000 in Scientific Notation, is written as 103
10,000 is a 1 followed by 4 zeros, so 10,000, in Scientific Notation, is written as 104
104 = means "10 to the 4th power" or "4 multiples of 10"
104 = 10 x 10 x 10 x 10 = 10,000
Express a number many ways.
Teach 4 people how to translate Scientific Notation into a number!
8 x 102 means to find the bill that has 2 zeros: $100
and get 8 of them.
Altogether, you have 8 hundred =
$800.
When you express a number as it’s power of ten, you are writing it in Scientific Notation.
Scientific Notation is a shortcut for writing numbers so that you don’t have to write all the zeros!
Practice scientific notation into bills!
Express each number many ways:
With money: 4 ten dollar bills
In words: Forty
In standard form: $40.
With the SI Symbol: 4 da
4 x 100 means to find the bill that has 0 zeros: $1
and get 4 of them.
Altogether, you have 4 ones =
$4
3 x 100
6 x 100
1 x 100
5 x 100
3 x 101 means to find the bill that has 1 zeros: $10
and get 3 of them.
Altogether, you have 3 tens =
$30
4 x 101
7 x 101
2 x 101
9 x 101
8 x 102
5 x 102
3 x 102
1 x 102
4 x 103
7 x 103
2 x 103
9 x 103
7 x 104
4 x 104
0 x 104
6 x 104