CPhill

(x+18)/4=8   multiply both sides by 4

x + 18 = 32   subtract 18 from both sides

x = 14

20/26 = 10/13 = about .769 = about 76.9%

Just "flip" the fraction over and change the exponent to a positive...to see why this is so, consider......

(2/3)^-3 =  1/(2/3)³ = 1/(8/27) = (27/8)  = (3/2)³...........voila !!!!

!000 x 10.5 =

(1 x 10³ ) x (1.05 x 10¹ ) = 1.05 x 10⁴

481/74 = 6.50  = 650%

0.000000376 =

3.76 x 10^-7  

It provides a convention (protocol) for performing mathematical operations in a specified order (known as the order of precedence).....for instance.....if we had......

13 + 6 x 7    ..... which operation should be carried out first??

We might think that we would add first and then multiply, but this is incorrect...the order of operations tells us to perform the multiplication and then the addition. Without this structure, there would be chaos in trying to determine the "right" answer!!!  The first (incorrect) result would be 133....the second (correct result) = 55.....see the difference??

897,000,000 = 897,000,000.

Write the non-zero part of the number and put a decimal after the first non-zero digit of this....so we have....

8.97 .......and we will multiply this by 10 raised to some power

Now, we would have to move the decimal eight places to the right to return the original number....and this is the exponent (power) that we will put on 10 in our multiplication....so we have....

8.97 x 10⁸

Not a proportion...just a fraction....so we have.....

(15 ounces of lead)/(80 total ounces)  = 3/16 = .1875  or 18.75%

x^-.3=.3714   ...we can write this as

1/(x^3/10) = 3714/10000  .... and when two fractions are equal, their reciprocals are equal, too...so we have...

(x^3/10) = 10000/3714    ......exponentiate both sides to the (10/3) power

x = (10000/3714)^(10/3) = about 27.156     (we could have also solved this problem using logs, too)