STANDARD FORMS (Scientific Notations)

STANDARD FORMS.

Hello lovely learners, Glad you are doing well. Today we are going to treat a mathematics topic that is worrying most of us. This is standard form. Most of the time, we solve questions and they ask us to leave our final answer in standard form or scientific notations. This is where most students find it difficult. So let us dive in.

First of all, standard form is a way we represent numbers that may be too big or too small to write or mention. Imagine solving a questions and getting a decimal like 0.000045. This can be easily written is standard form as 4.5 × 10^-5 . This is quite simple right? Well let’s get started

A standard form (also called scientific notation) refers to a way to write very large or very small numbers in a more compact and easier-to-read form. It uses powers of 10.

Here's the basic structure of a number in scientific notation:

·Coefficient: A number between 0 and 10.

·Base: 10.

·Exponent: A positive or negative integer.

Lets explain each point. First let us take the coefficient.

It is a number between 0 and 10. It can be a decimal. When we have a number like 245, we have to change it so that it becomes a number between 0 and 10. This is done by bring the decimal point behind the first non-zero digit. This means the point will come between 2 and 4. So it becomes 2.45. In the case of 0.000045, the point will come between 4 and 5 and we get rid of all the leading zeros i.e. 4.5. 274000 will also become 2.74 and so on.

The base is always 10. This means that after finding the coefficient, the next thing is to multiply it by 10.

The exponent can be a positive or negative integer depending on the number given.

Now let us know the steps of changing a number into standard form

To convert a number to scientific notation:

1.      Move the decimal point: Move the decimal point to a position after the first non-zero digit.

2.      Count the moves: Count how many places you moved the decimal point.

3.      Write the number: Write the number with the decimal point in the new position.

4.      Multiply by 10ⁿ: Multiply the number by 10 raised to the power of the number of places you moved the decimal point. If you moved it to the right, the exponent is negative; if you moved it to the left, the exponent is positive.  

For example:

·To convert 345,000 to scientific notation:

o    Move the decimal point to after the 3 i.e. 3.45

o    Count the moves: 5 places to the left (positive)

o    Write the number: 3.45

o    Multiply by 10ⁿ i.e.  3.45 x 10⁵

·         To convert 0.0025 to scientific notation:

o   Move the decimal point to after 2 i.e. 2.5

o   Count the moves: 3 places to the right (negative)

o   Write the number: 2.5

o   Multiply by 10ⁿ i.e 2.5 x 10^-3.

·         Anytime a number is already in standard form just write the power as 10⁰

o   Example 2.356 is the same as 2.356 x 10^0.

o   Note that 10⁰ = 1 and so its like multiplying a number with one, the value doesn’t change.

Now try solving these questions for me. Send your answers to my e-mail stakhanovite91@gmail.com or leave them under the comment section. Remember you can also contact us on 0503898729 (WhatsApp only) for any questions you have.

1.      25679

2.      0.000372

3.      1287.3

4.      87

5.      400000

6.      2.56

7.      0.14768

8.      7 million

9.      2,467,000,000

10.  0.000000456

Now let us look at how to change from standard form to normal form.

·  Multiply: Multiply the coefficient by 10 raised to the power of the exponent.

·  Move the decimal point: Move the decimal point to the right if the exponent is positive; move it to the left if the exponent is negative. The number of places you move the decimal point is equal to the absolute value of the exponent.

Solving the 10ⁿ is very easy. If the exponent is positive, just add the number of zeros equivalent to the exponent. For example, 10⁴ = 10000; 10⁷ = 10000000 and so on.

If the exponent is negative then make it a fraction where the denominator is done same way as we did up here. For example 10^-4 = ¹/₁₀₀₀₀; 10^-2 = ¹/₁₀₀ and so on.

After that just multiply the coefficient to the power of 10 solved.

For example 7.9 x 10^-3 can be solved using this method

1.      10^-3 = ¹/₁₀₀₀

2.      Multiply this by the coefficient 7.9 i.e. 7.9 x ¹/₁₀₀₀.

3.      This gives 0.0079.

·2.78 x 10⁵ will give 2.78 x 100000

o    This will give us 278000.

Now try these questions for me

Change these into decimal numerals

1.      2.98 x 10⁷

2.      4.6 x 10^-4

3.      2.17 x 10³

4.      1.38 x 10^-1

5.      2.7 x 10¹

That’s all we have for today. Make sure you try more examples as practice makes perfect. Check out other useful topics on this blog and share with your friends.

Until we meet again, it is your teacher DNA wishing you all the best.