Scientific notation is a way of writing numbers as a coefficient multiplied by a power of ten. It makes large and small numbers easier to work with in calculations. To write a number in scientific notation, the decimal is moved to place it between 1 and 10, and the number of places the decimal is moved determines the exponent. For example, 4,600,000,000,000 meters written in scientific notation is 4.6 × 1012. The number of significant figures refers to the meaningful digits in the coefficient and depends on placement of zeros. Rules for addition, subtraction, multiplication and division specify keeping the same number of significant figures as the least precise measurement or factor.

1. By Javed Ali Buller

2. Scientificnotationisa valuewrittenas asimplenumbermultipliedbya power
of ten.It isanother wayof writingnumbers.Italsomakes calculatingthese
numberseasier.
Correct scientificnotationhas acoefficientthat islessthan10and greater
thanorequalto 1.Thatcoefficientisthenmultipliedbya power often.
Example:
46000=4.6x104

3. The steps for writingscientific notationare rather simple. Let's
go over themby actuallychangingnumbers into scientific
notation.
Example:
The distance betweenEarth and Neptuneis
4,600,000,000,000 meters. How do we write it in Scientific
Notation?

4. Placethe decimal pointafter the first whole number digit
and dropthe zeros. The number "4" is the first whole
number.
So:
4.600,000,000,000

5. Findtheexponent.To do this,count thenumberofplaces fromthe
new decimalpointtotheendofthe number.This decimalpointis
12 placesfrom theendofthenumberor wherethe decimalwas
originally.
So:
4.600,000,000,000.
NewDecimal Point Original Decimal Point

6. Rewritethenumberbymultiplyingitbya poweroften.
*Drop allzeros andwriteyour number.Thisnumbermustbemultipliedbya
powerof10.
4.600,000,000,000=4.6x 10
*Yourexponentwillbethenumberofplacesthatthedecimalpointwas
moved. Sincethedecimalpointwasmoved12 places,theexponentwillbe
"12".
4.6x 1012

7. The term significant figures refers to the numberof
importantsingle digits
(0 through 9)inthe coefficientof an expressionin
ScientificNotation.

8. 1. All nonzero digits aresignificant:
1.234 g - has4 significantfigures,
1.2 g - has2 significantfigures.
2. Zeroesbetweennonzero digits are significant:
1002 kg -has 4 significantfigures,
3.07 mL -has 3 significantfigures.

9. 3. Leading zeros to the left of the first nonzerodigits are not
significant;such zeroes merely indicatethe position of the
decimalpoint:
0.001mg- hasonly1significantfigure
0.012g-has2significantfigures.
4. Trailingzeroes that arealso to the right of a decimal point
ina number are significant:
0.0230ml- has3significantfigures
0.20g -has2significantfigures.

10. 5. When a number ends in zeroes that are not to the
right of a decimalpoint, the zeroes arenot
necessarilysignificant:
190 miles may be 2 or 3 significantfigures
50,600 calories may be 3, 4, or 5 significantfigures.

11. 1. In addition and subtraction, the result is roundedoff to the last
commondigit occurringfurthest to the right in all components.
Another way to state this ruleis as follows:in addition and
subtraction, the result is roundedoff so that it has the same
number ofdigits as the measurement having the fewestdecimal
places (counting fromleft to right). Forexample,
100 – 3 SF
+ 23.645 – 5 SF
123.645 = 124

12. 2. In multiplicationanddivision, theresultshouldberounded
off so asto havethesamenumberof significantfigures asin
thecomponent withthe leastnumberof significantfigures.
Forexample,
12.25 – 4 SF
X 3.0 – 2 SF
36.75 = 37