Scientific Notation
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 each section (ex. Thousand); the value of each place (1, 10, 100); the prefix that represents the SECTION (ex. kilo-); and the 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 = .1); the prefix (deci-); and the symbol (ex. d).
(3) Study the SI (International Standard) Number Chart that shows the power of 10, the decimal form, prefix, and symbol for each place value.
(4) Scientific Notation is a short way to express a number without writing all of the digits.
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 1
10 is a 1 followed by 1 zero, so 10, in Scientific Notation, is written as 10
100 is a 1 followed by 2 zeros, so 100, in Scientific Notation, is written as 10.
Each time you MULTIPLY 1 by 10, add a 0 to the UNIT 1: 1 × 10 = 10
10 × 10 = 100
100 × 10 = 1000 ...
Each 10 is a MULTIPLIER and a FACTOR. The result is the PRODUCT.
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 10
10,000 is a 1 followed by 4 zeros, so 10,000, in Scientific Notation, is written as 1 × 10.
It is read, "10 to the 4th power". It means "4 multiples of 10".
10 = 10 × 10 × 10 × 10 = 10,000
Express a number many ways.
Teach 4 people how to translate Scientific Notation into a number.
3 × 10 find the bill that has 2 zeros: $100
and get 3 of them.
Altogether, you have 3 hundred =
$300.
When you express a number as it’s power of ten, you are writing it in Scientific Notation.
Model numbers with bills:
Express each number many ways:
Scientific Form: 4 × 10 = 4 × $10 = $40
Money: 4 ten dollar bills
Words: Forty
Standard Form: $40.
SI Symbol: 4 da
4 x 10 means find the bill that has 0 zeros, which is $1., and get 4 of them.
Altogether, you have 4 ones = $4.
3 x 10 = $3.
6 x 10 = $6.
1 x 10 = $1.
5 x 10 = $5.
3 x 10 means to find the bill that has 1 zero: $10
and get 3 of them.
Altogether, you have 3 tens = $30.
4 x 10 =
7 x 10 =
2 x 10 =
9 x 10 =
8 x 10 =
5 x 10 =
3 x 10 =
1 x 10 =
4 x 10 =
7 x 10 =
2 x 10 =
9 x 10 =
7 x 10 =
4 x 10 =
0 x 10 =
6 x 10 =
4
2
1
0
0
0
0
0
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
6
6
