Algebra Honors (Period 6 & 7)

Scientific Notation 7-10
Scientific notation makes it easier to work with either very large numbers or very small numbers. To write a positive number in scientific notation, you express it as the product of a number greater than or equal to 1 BUT less than 10 AND an integral power of 10.
When a positive number greater than or equal to 10 is written in scientific notation, the power of 10 is positive. When the number is less than 1, the power of 10 will be negative.

Scientific notation consists of two parts
1≤ x< 10 × POWER¹⁰
for example
58,120,000,000
Move the decimal point left 10 spaces to between the 5 and the 8 to get a number BETWEEN 1 and 10
5.8
so 5.8 × 10¹⁰
0.00000072
Move the decimal point 7 places to the right to get a number between 1 and 10
7.2
7.2 × 10^-7

Numbers written in scientific notation can be multiplied and divided easily by using the rules of exponents
Simplify. Keep your answers in scientific notation
3.2 × 10⁷/2.0 × 10⁴
= 3.2/2.0 ×10⁷/10⁴
=1.6 × 10^7-4
=1.6 × 10³

(2.5 × 10³)(6.0 × 10²)
=(2.5 ×6.0) × (10³ × 10²) Add exponents
= (15)(10³⁺²)
=15 × 10⁵
But wait 15 is not between 1 and 10
15 itself is 1.5 × 10¹
so it becomes
1.5 ×10¹× 10⁵
1.5 × 10¹⁺⁵
=1.5 × 10⁶
The distance from the sun to Mercury is approximately 6 × 10⁸ km.
The distance from the sun to Pluto is approximately 5.9 × 10⁹ km
Find the ratio of the first distance to the second distance
Distance from sun to Mercury
Distance from sun to Pluto
6 × 10⁸
5.9 × 10⁹
= 6/5.9 × (10⁸)/10⁹

= 6/5.9 ×10^8-9
6/5.9 ×10^-1
=6/5.9 ×1/10
= 6/59

You learned expanded notation in 6th grade... but a review of writing numbers in expanded notation using powers of 10 follows:
8572 = 8000 + 500 + 70 + 2
=8(10³) + 5(10²) + 7(10¹) + 2(10⁰)

0.3946 = 0.3 + 0.09 + 0.004 + 0.0006
= 3(10^-1) + 9(10^-2) +4(10^-3) + 6(10^-4)

25.03 = 2(10¹) +5(10⁰) + 0(10^-1) + 3(10^-2)

The metric system is also based on powers of TEN.
To change from one metric unit to another, you simply multiply by a power of 10.
Remember:
King Henry Died By Drinking Chocolate Milk
1 km = 10³m = 1000m
1mL =10^-3 L = 1/1000 L