Converting from decimals to scientific notation
Converting from decimals to scientific notation
Converting from decimals to scientific notation
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CONVERTING FROM SIMPLE NUMBERS TO EXPONENTIAL NOTATION<br />
STEP 1 – move the decimal point <strong>to</strong> the right of the 1 st non-zero digit:<br />
e.g. 0.00105 OR 1,050<br />
1.05 1.05<br />
STEP 2 – determine the power <strong>to</strong> which 10 is raised (i.e., 10 n ) <strong>to</strong> compensate for<br />
moving the decimal:<br />
The power is going <strong>to</strong> be equal <strong>to</strong> the number of places you moved the decimal<br />
(10 3 in the examples above). You need only <strong>to</strong> determine the sign (+ or -) of the<br />
exponent. This can be determined in 2 ways, whatever works best for you:<br />
1) If the original number is less than 1, the exponent is negative (-),<br />
if the original number is greater than 1, the exponent is positive (+).<br />
OR<br />
2) If you moved the decimal <strong>to</strong> the right, the exponent is negative (-),<br />
if you moved the decimal <strong>to</strong> the left, the exponent is positive (+).<br />
Either way:<br />
0.00105 = 1.05 x 10 -3<br />
1,050 = 1.05 x 10 3<br />
Some things <strong>to</strong> remember about the conventions of writing numbers:<br />
-if there is no decimal in the number, it is after the last digit (1,050 = 1050.0)<br />
-all zeroes after the last non-zero digit <strong>to</strong> the right of the decimal can be dropped<br />
(e.g., 1.050 = 1.05)<br />
-all simple numbers less than 1 are written with a zero <strong>to</strong> the left of the decima1<br />
(.105 = 0.105)<br />
CONVERTING FROM EXPONENTIAL NOTATION TO SIMPLE NUMBERS<br />
You simply move the decimal a number of places equal <strong>to</strong> the exponent. If the exponent is<br />
negative, the number is less than one and the decimal should be moved <strong>to</strong> the left:<br />
1.05 x 10 -3 = 0.00105<br />
If the exponent is positive, the number is greater than one and the decimal should be moved <strong>to</strong><br />
the right:<br />
1.05 x 10 3 = 1,050
CONVERTING UNITS WITHIN THE METRIC SYSTEM<br />
First and foremost, you need know (i.e., memorize) what each metric prefix represents:<br />
mega- (M) = 10 6 units<br />
kilo- (k) = 10 3 units<br />
BASE UNIT (no prefix) = 1 (i.e., 10 0 ) unit<br />
deci- (d) = 10 -1 units<br />
centi- (c) = 10 -2 units<br />
milli- (m) = 10 -3 units<br />
micro- (μ) = 10 -6 units<br />
nano- (η) = 10 -9 units<br />
When converting <strong>from</strong> one metric unit <strong>to</strong> another, simply move the decimal point a number of<br />
places equal <strong>to</strong> the difference* between the exponents associated with each prefix. When<br />
converting <strong>from</strong> larger <strong>to</strong> smaller units, the number should increase therefore the decimal<br />
should move <strong>to</strong> the right:<br />
e.g. 105 kg (105 x 10 3 g) = ____________ mg (? x 10 -3 g)<br />
-the difference between the exponents for each prefix is 6 (3 – (–3) = 6)<br />
-since you’re converting <strong>from</strong> larger <strong>to</strong> smaller units, the decimal is moved<br />
6 places <strong>to</strong> the right:<br />
105 kg (105 x 10 3 g) = 105,000,000 mg (105,000,000 x 10 -3 g)<br />
When converting <strong>from</strong> smaller <strong>to</strong> larger units, the number should decrease therefore the<br />
decimal should move <strong>to</strong> the left:<br />
e.g. 105 mg (105 x 10 -3 g) = ____________ kg (? x 10 3 g)<br />
-the difference between the exponents for each prefix is –6 (–3 – 3 = –6)<br />
*don’t worry about whether the difference is + or –<br />
-since you’re converting <strong>from</strong> smaller <strong>to</strong> larger units, the decimal is moved<br />
6 places <strong>to</strong> the left:<br />
105 mg (105 x 10 -3 g) = 0.000105 kg (0.000105 x 10 3 g)<br />
*The difference between 2 numbers is one number subtracted <strong>from</strong> another. Remember that<br />
subtracting a negative number is the same as adding a positive number (e.g., 3 – (–3) = 6). The<br />
easiest way <strong>to</strong> think of this is <strong>to</strong> use a number line:<br />
-6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6<br />
The difference between 2 numbers for our purposes is simply the number of positions on the<br />
number line it takes <strong>to</strong> go <strong>from</strong> one number <strong>to</strong> the other.<br />
(e.g., <strong>from</strong> –3 <strong>to</strong> +3 is 6 places, <strong>from</strong> +3 <strong>to</strong> –3 is also 6 places)