Scientific Notation
A way scientists handle very large and very small numbers using powers of 10.
Written in the form a x 10^b
Examples:
Write in Scientific Notation
a) 4830000000 à4.83 x 10^9
b) 0. 000056 à 5.6 x 10^-5
Write in Standard Form:
a) 6.25 x 10^4 à 62500
b) 8.9 x 10 ^-9 à 0.0000000089
- Addition and Subtraction
o All numbers must be converted to the same power of 10
o The digits are then added or subtracted
- Multiplying and Dividing
o Digits are multiplied or divided
o Exponents are added or subtracted.
* Keep exponent laws in mind*
Quiz Yourself!!
Here is a great website to practice multiplying, adding, subtracting and expressing numbers in scientific notation:
*Note* Calculators can be used to make this process easier. Use the EXP/ E / x 10^ buttons.
Even More Unitary Rates
- Convert the unit which is squared or cubed
If 1m= 100cm
1m^2 = 10 000 cm^2 (100 x 100)
1m^3 = 1 000 000 cm^3 (100 x 100 x 100)
Ex. Convert
a) 9.6m^3 à to km^3
1000m= km
10^9 m^3 = km^3
9.6 m^3 x (km^3/10^9 m^3)
= 9.6 x 10^-9 km^3
b) 6.5 dm^2 à Gm^2
dm à mà Gm
10^2 dm^2 = 1m^2 (10 dm = 1m à 10^2dm = 10m^2)
10^18 m^2 = 1 Gm^2 ( 10^9m = 1Gm à 10^18 m^2 = 1Gm)
= 6.5 x 10^-20 Gm^2
Here are some examples to try on your own:
a) Convert 7.5 dm^2 to Mm^2
b) Convert 54 mm to pm
c) Convert 5.5 m^3 to km^3
d) Convert 12.4 L to mL
By Candace
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