Standard Form

A standard form is a convenient way to write a very large or very small numbers .
It is quite similar to indices whereby the number has a base and index.

A important observation from me . Students often forget whether to move the decimal place to the left or to the right.


So, i came up with steps to write a number in standard form

1. Move the decimal point until one gets a number between 1 to 10
2. Count the number of places one moves the decimal point.
The exponent is POSITIVE if one moves the point to the left while the exponent is NEGATIVE if one moves the point to the right! Take note!

Also, students must remember that a number expressed in standard form is a product of a number between 1 and 10, therefore , it is also a product of 10. I have 3 examples.

1 . 3862.9 = 3.8629 x 10^3 . Here , we move the decimal 3 places to the left.
2. 978000= 9.78 x 10^5 . Here , we move the decimal 5 places to the left.
3. 0.000568 = 5.68 x 10^-4 . Here , we move the decimal 4 places to the right.

Below, i have started the first steps for a few questions . Why don't you try to solve it?
Addition :

3.2 x 10^3 + 2.5 x 10^2
= 32 x 10^2 + 2.5 x 10 ^2 ... Here we extract the lowest power of 10 and change them to the same power

Subtraction :

5.68 x 10^-3 - 4.3 x 10^-4
= 56.8x 10^-4 - 4.3 x 10^-4
Here we extract the lowest power of 10 . also, we do that by moving the decimal to the left .

Multiplication :

(2 x 10^-2) x ( 5.6x 10^5 )
= (2 x 5.6) x ( 10 ^-2 x 10 ^5 ) ... remember rules of indices? it works here ! Collect all the powers of 10 together and the rest into another group .

Then ...

= 11.2 x 10^3
= 1.2 x 10^4 ... Here students must remember not to stop at 11.2 x 10^3. this is because it is a answer in standard form

Remember standard form = 1.0-9.99 x 10 ^something.



Questions


1. How do we use a calculator to evaluate a number in standard form?


The main problem that students face when solving standard form questions are when the do not know how to type into their calculator, hence causing them to know how to solve the question but not knowing how to use the calculator to derive at the correct answer.


Ans: We use the EXP key on the calculator to evaluate a number in standard form.