Question

Calculate the value of (6.72 10^5)+ (3.2 x 10^4)
Give your answer in standard form.

Answer 1

`7.04\cdot 10^(5)` or 704,000

Explanation:

Standard Form of Numbers

Any number that we can write as a decimal number between 1.0 and 10.0, multiplied by a power of 10, is said to be in Scientific Notation. Some authors consider standard form and scientific form as the same, but others state that standard form is the common form of expressing numbers, i.e., a sequence of digits, separated by thousands by a comma, and separated from the decimal part by a dot.

We'll give here both answers.

We have to calculate:

`6.72\cdot 10^(5)+3.2\cdot 10^(4)`

Since the numbers don't have the same exponent, we must make them equal. Let's make the second number have an exponent of 5, by dividing by 10:

`6.72\cdot 10^(5)+3.2\cdot 10^(4)=6.72\cdot 10^(5)+3.2/10\cdot 10^(5)`

`6.72\cdot 10^(5)+3.2\cdot 10^(4)=6.72\cdot 10^(5)+0.32\cdot 10^(5)`

Now we add:

`6.72\cdot 10^(5)+3.2\cdot 10^(4)=7.04\cdot 10^(5)`

It's correctly expressed in scientific notation. Now to convert to 'standard form', multiply by
`10^5=100,000`:

`6.72\cdot 10^(5)+3.2\cdot 10^(4)=7.04*100,000=704,000`