Simplify (8.33×103)+(4.1×105) giving your solution in scientific notation?

2 Answers
EZ as pi
Oct 6, 2016

4.1833×105

Explanation:

In Algebra:
3x4+8x4=11x4 ← add like terms

3x4+5x6=3x4+5x6
These terms cannot be added because the indices are not the same so they are not like terms

In scientific notation you do exactly the same:

3.5×107+1.3×107=4.8×107

But sometimes adding creates a small problem:

4.9×105+7.3×105=12.2×107 ← must be one digit
××××××x.x=1.22×108 ← adjusted

(8.33×103)+(4.1×105) ← cannot be added like this
But unlike algebra, in scientific notation, you can change the value of the index by moving the decimal point.

If it moves to the left, the index increases.
If it moves to the right, the index decreases

=(8.33×103)+(4.1×105) ← make indices the same

=0.0833×105+4.1×105 ← change to the bigger index

=4.1833×105 ← add like terms

What you want to avoid is writing the numbers in numeral form (with lots of zero's) adding them and then changing them back to standard form. While that might work for small indices, it is simply not practical with bigger indices!

Tony B
Oct 6, 2016

4.1833×105

Explanation:

Given: (8.33×103)+(4.1×105)..........Equation(1)

Note that 102×103→102+3=105

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write equation(1) as:

(8.33×103×1)+(4.1×105)

However, 1 is the same as 102102 giving:

(8.33×103×102102)+(4.1×105)

Swap round the numbers (condition of being 'commutative' )

(8.33102×103×102)+(4.1×105)

But 8.33102=0.0833 and 102×103=105 giving

(0.0833×105)+(4.1×105)

Factor out the 105

105(0.0833+4.1)=4.1833×105

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