Scientific Notation

Very large or very small numbers are written in the scientific notation for convenience and to save space. That is to say,
n × 10x where 1 ≤ n < 10

(n is decimal) and the exponent, x, is an integer, positive or negative




This is also commonly known as the standard form, or exponential notation. You'll find that this notation is used quite frequently by all sorts of people, particularly scientists, mathematicians, doctors and engineers. Even calculators use this form because it makes handling large numbers very easy.

Examples
a) 2,100,000 = 2.1 × 106

Steps:
i) Place the decimal point to obtain a number between 1 and 10, then
ii) count the digits to the right to get the power of 10.



b) 4,730 = 4.73 × 103



c) 0.0000003 = 3.0 × 10-7

Steps:
i) Place the decimal point to obtain a number between 1 and 10, then
ii) count the digits from the original decimal point to the new one.



d) 0.00152 = 1.52 × 10-3



(a) & (b) are examples of very large numbers
whereas (c) & (d) are examples of very small numbers


Multiplication in scientific notation


Steps:
i) Multiply the numbers that are between 1 and 10, then
ii) add the exponents on the tens, and finally
iii) adjust, if necessary, to express correctly in standard form.

Examples:
In general,
(n × 10x) × (m × 10y) = mn × 10x + y




Division


Steps:
i) Divide the numbers that are between 1 and 10,
ii) subtract the exponents on the tens, then
ii) adjust, if necessary, to express correctly in standard form.

In general,

Examples



Addition & Subtraction in Standard Form


If the numbers to be added or subtracted have the same exponents, then direct addition or subtraction can be performed.



Examples


For examples (iii) & (iv) the final answer needs to be adjusted to standard form.



If the exponents are different, then adjustments have to be made. Usually the larger numbers are converted to accommodate the smaller numbers. After addition or subtraction has been carried out, the final answer also needs to be adjusted so as to be correctly expressed in standard form.

Examples




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I believe there is a typo on the section of Addition and subtraction in Standard form. On example ii) the answer 2.94 should be 1.94 Damien: Yes, it …

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