I need help with scientific notation

Question

I need help with scientific notation.

Answer 1

Scientific notation is the common way that very large numbers are expressed.

 

First let me explain that every number contains what we would call a decimal point. First there are the obvious numbers like

 

1.5, 10.2, 156.4, 12.4853, .002876, .943

 

However, there are other numbers that we do not always see the point. For these numbers the point is at the end.

for example

 

5, 70, 8432, 803, 9272, 1000

 

It is important to note that after a decimal point you can add 0's after the last number in the sequence without changing it.

 

12.57 is the same as 12.5700000000000,  also 39 is the same as 39.000000000

 

you can also add 0's in front of the fore most number before a decimal point without changing it.

 

2389 is the same as 00000002389, also .0273 is the dame as 0000000.0273

 

with that knowledge when you multiply something by 10 you will move that decimal point to the right once

 

12*10 = 120

 

23.67*10 = 236.7

 

if you have the 10 to some power such as 10^3 in actuality you have 10*10*10 (which if multiplied by something will move the decimal point over by 3)

so

 

27.893*10^3 = 27893    also    56*10^5 = 5600000

 

if you noticed what ever the exponent, it is the same number of times you move the decimal point to the right. In likeness when you multiply a number times 10 to a negative exponent, you will move the decimal point to the left.

 

239.92*10^-2 = 2.3992   also    .938*10^-5 = .00000938

 

finally to get an number into what would be considered scientific notation you would move the decimal point to where there would only be one number to the left of the decimal point.

 

so 578 would be 5.78,     .009432 would be 9.432

 

now you will multiply this new number by 10 to the power of an exponent to move the decimal back to its original position.

so using the examples before

 

578 would be 5.78*10^2 ,   and  .009432 would be 9.432*10^-3

 

 

The reason this exists is so if you have very large number such as

 

24,500,000,000,000,000,000,000,000,000,000

 

it can be expressed as

 

2.45*10^31