Converting from decimals to scientific notation

CONVERTING FROM SIMPLE NUMBERS TO EXPONENTIAL NOTATION
STEP 1 – move the decimal point to the right of the 1 st non-zero digit:
e.g. 0.00105 OR 1,050
1.05 1.05
STEP 2 – determine the power to which 10 is raised (i.e., 10 n ) to compensate for
moving the decimal:
The power is going to be equal to the number of places you moved the decimal
(10 3 in the examples above). You need only to determine the sign (+ or -) of the
exponent. This can be determined in 2 ways, whatever works best for you:
1) If the original number is less than 1, the exponent is negative (-),
if the original number is greater than 1, the exponent is positive (+).
OR
2) If you moved the decimal to the right, the exponent is negative (-),
if you moved the decimal to the left, the exponent is positive (+).
Either way:
0.00105 = 1.05 x 10 -3
1,050 = 1.05 x 10 3
Some things to remember about the conventions of writing numbers:
-if there is no decimal in the number, it is after the last digit (1,050 = 1050.0)
-all zeroes after the last non-zero digit to the right of the decimal can be dropped
(e.g., 1.050 = 1.05)
-all simple numbers less than 1 are written with a zero to the left of the decima1
(.105 = 0.105)
CONVERTING FROM EXPONENTIAL NOTATION TO SIMPLE NUMBERS
You simply move the decimal a number of places equal to the exponent. If the exponent is
negative, the number is less than one and the decimal should be moved to the left:
1.05 x 10 -3 = 0.00105
If the exponent is positive, the number is greater than one and the decimal should be moved to
the right:
1.05 x 10 3 = 1,050

CONVERTING UNITS WITHIN THE METRIC SYSTEM
First and foremost, you need know (i.e., memorize) what each metric prefix represents:
mega- (M) = 10 6 units
kilo- (k) = 10 3 units
BASE UNIT (no prefix) = 1 (i.e., 10 0 ) unit
deci- (d) = 10 -1 units
centi- (c) = 10 -2 units
milli- (m) = 10 -3 units
micro- (μ) = 10 -6 units
nano- (η) = 10 -9 units
When converting from one metric unit to another, simply move the decimal point a number of
places equal to the difference* between the exponents associated with each prefix. When
converting from larger to smaller units, the number should increase therefore the decimal
should move to the right:
e.g. 105 kg (105 x 10 3 g) = ____________ mg (? x 10 -3 g)
-the difference between the exponents for each prefix is 6 (3 – (–3) = 6)
-since you’re converting from larger to smaller units, the decimal is moved
6 places to the right:
105 kg (105 x 10 3 g) = 105,000,000 mg (105,000,000 x 10 -3 g)
When converting from smaller to larger units, the number should decrease therefore the
decimal should move to the left:
e.g. 105 mg (105 x 10 -3 g) = ____________ kg (? x 10 3 g)
-the difference between the exponents for each prefix is –6 (–3 – 3 = –6)
*don’t worry about whether the difference is + or –
-since you’re converting from smaller to larger units, the decimal is moved
6 places to the left:
105 mg (105 x 10 -3 g) = 0.000105 kg (0.000105 x 10 3 g)
*The difference between 2 numbers is one number subtracted from another. Remember that
subtracting a negative number is the same as adding a positive number (e.g., 3 – (–3) = 6). The
easiest way to think of this is to use a number line:
-6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6
The difference between 2 numbers for our purposes is simply the number of positions on the
number line it takes to go from one number to the other.
(e.g., from –3 to +3 is 6 places, from +3 to –3 is also 6 places)