Algebra Period 4

Scientific Notation 5-4



You've had this since 6th grade!
It is just a bit more complicated
You restate very big or very small numbers using powers of 10 in exponential form

Move the decimal so the number fits in this range:
less than 10 and greater than or equal to 1
That is 1 ≤ n < 10
Scientific notation is the product of two factors
one of the factors is a number that is 1 ≤ n < 10 and the other factor is a power of ten

Count the number of places you moved the decimal and make that your exponent

Very big numbers - exponent is positive

Very small numbers (decimals) - exponent is negative (just like a fraction!)


Remember that STANDARD notation is what you expect (the normal number)



When you multiply or divide scientific notations, use the power rules!

Just be careful that if your answer does not fit the scientific notation range, that you restate it.

(2.5 x 10 ^-3)(4.0 X 10 ^-8)
multiply the first factors or (2.5)(4.) and multiply the powers of ten
(10 ^-3)(10 ^-8)

(2.5)(4)= 10
so initially you have 10 X 10 ^-11
but 10 does not fall into the required 1 ≤ n < 10
so changed 10 into scientific notation or 1.0 X 10¹
so you have 1.0 X 10¹ X 10 ^-11
or 1 X 10 ^-10

What about
6.0 x 10 ⁷
3.0 X 10²
First divide 6.0/3.0 = 2.0
and use the exponent rules of 10 ^{7 -2} or 10⁵
so 2.0 X 10⁵

4.2 X 10⁵
2.1 X 10³

= 2 X 10²

2.5 X 10 ^-7
5.0 X 10 ⁶
first 2.5/5 = 0.5 and 10^-7/10⁶ = 10^-7-6 = 10^-13
so initially you have
0.5 x 10^-13 but 0.5 is not within 1 ≤ n < 10
so change 0.5 to scientific notation
5.0 X 10 ^-1 and mult that by 10^-13
5 X 10 ^-14

Math 6H ( Periods 3, 6, & 7)

Dividing Decimals 3-9


According to our textbook-
In using the division process to divide a decimal by a counting number, place the decimal point in the quotient directly over the decimal point in the dividend.

Check out our textbook for some examples!!

When a division does not terminate-- or does not come out evenly-- we usually round to a specified number of decimal places. This is done by adding zeros to the end of the dividend, which as you know, does NOT change the value of the decimal. We then divide ONE place beyond the specified number of places.

Divide 2.745 by 8 to the nearest thousandths.
See the set up in our textbook on page 89. Notice that they have added a zero and the end of the dividend ( 2.745 becomes 2.7450) because you want to round to the thousandths and we need to go ONE place additional.
DIVIDE carefully!!

the quotient is 0.3431 which rounds to 0.343


To divide one decimal by another

Multiply the dividend and the divisor by a power of ten that makes the DIVISOR a counting number


Divide the new dividend by the new divisor

Check by multiplying the quotient and the divisor.

Tickets to the school play cost $5.25 each. THe total receipts were $651. How many tickets were sold?

Divide $651 by $5.25

that is, divide 651 by 5.25

or divide 65100 by 525.

124

So A total of 124 tickets were sold.


Check the textbook for the details to the division-- as it is impossible to do here!!

Algebra Period 4

Multiplying and Dividing Monomials 5-3

A monomial is an expression that is either a numeral, a variable , or a product of numerals and variables with whole number exponents. IF the monomial is just a numeral we call is a constant.

Some examples: 4x³, -7ab, y (1/2)x⁵ and 2x⁴y

The following are NOT monomials
1/y, x^1/2, x² +4, y² + 2y + 4

Multiplying monomials - use the properties of rational numbers and the properties of exponents:
(3x)(4x) = 12x²

(3x²)(-x) = (3x²)(-1x)
= (3)(-1)(x²)(x)
=-3x³

(-3a)(4a²)(-a⁴ = (-3)(4)(-1)(a)(a²)(a)
=12a⁷

Dividing is similar-- Use the properties of rational numbers and the properties of exponents:

x⁵/x² = x^5-2 = x³

4x²/5x⁷ = (4/5)x^2-7 = (4/5)x^-5 OR
(4/5x⁵)

12m⁵/4m³ = 3m²
BUT
4m⁵/12m³ = m²/3

Be careful Keep the RULES Separate!! Don't mix up your exponent RULES with what you know previously for rational numbers!!