What are the 3 rules for writing numbers in standard form?

It can be expressed in the form X*10^n

X must be a number between 1 and 10

n must be a whole number

Standard form always uses base 10

I would call these steps rather than rules and there are 5 steps, but I was taught these when I was learning, it has never led me astray and I have passed this on to anyone I have taught standard form to :)

Step 1: Write down the first digit of the number

Step 2: Add a decimal point and write the remaining numbers

Step 3: Count the number of digits after this decimal point - this is number (power) 10 is raised to

Step 4: Rewrite the decimal to the accuracy the question has asked for e.g. 2 dp, 3 sf

Step 5: Add in your x 10 and your power - all done!

Example: Write 804569837 in standard form to 3sf

Step 1: 8

Step 2: 8.04569837

Step 3: 04569837 = 8 numbers

Step 4: 8.04569837 = 8.05 3sf

Step 5: 8.05 x 10^8

Note: Do not forget the different between decimal point and significant figure accuracy, and when a zero is significant!

Hope this helps :)

First step: Make sure you understand what the layout of standard form is:

Number less than 10 x 10 to the power of how many decimal places it moves.

Second step: look at your number. eg 450000

What numbers in here can you make less than 10?

45? not less than 10!

4.5! Yes! That's less than 10

Okay! now next step: How many places did the invincible decimal place move for you to get to 4.5

Remember the invincible decimal place is right at the end of the number 450000.

If you count now, that's 5 places.

So now put it into your standard form equation.

4.5 x 10^5

And you're done!

A standard form number takes the form of A x 10^B

1. A is a number that must be between 1 and 10, including 1 but excluding 10. It can be a whole number or a decimal number.
2. A standard form number always uses a base of 10.
3. B is the power of 10 which can be a positive or negative number, but it must be a whole number.

A number written in standard form is written as A x 10^n

Where A is a number bigger than or equal to 1 and less than 10.

n can be any positive or negative integer.

you need to start with a number between 1 and 10

then you need to multiply by 10

add the relevant power

write together

The rules for writing a number in standard form are as follows:

A number in standard form will be written as a×10^n ("a times 10 to the power on n").

1) 1 ≤ a <10 ("a must be greater than or equal to 1 and less than 10")

2) You need to use base 10 within the format

3) The value of n must be an integer (whole number)

Examples

Q) Write 345 in standard form

A) When starting with standard form, I would re-write the number as a multiple of 10 until the front number (value of a) meets the conditions above (see (1)):

345

= 34.5x10 = 34.5x10^1

=3.45x10x10 = 3.45x10^2

The final answer is 3.45x10^2

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Q) Write 0.00012 in standard form

Note: when dealing with negative values of n, you may use this to help you understand the process:

a×10^-n ≡  a÷10^n

For example 2× 10^-3 ≡ 2÷10^-3 = 0.002

Please be mindful that standard form must be written in the multiplication form, rather than left as division.

A) I will use the tip above to help understand the layout

0.00012

= 0.0012 ÷ 10 = 0.0012 ÷ 10^1

= 0.012 ÷10 ÷10 = 0.012 ÷ 10^2

=0.12 ÷ 10^3

=1.2 ÷ 10^4

= 1.2 ×10^-4

A number not written in standard form said to be in ordinary form (e.g. 1, 8, 231, 123.225, etc.)

1. express the sum as a whole number multiplied by 10
2. standard form uses base 10 (10 to the power of something x )
3. X- whole number

1. Normalize the Number: The number must be written as a decimal between 1 and 10. This involves placing the decimal point such that there is only one non-zero digit to the left of the decimal point.
2. 
   
3. Determine the Exponent: Count the number of places the decimal point has been moved from its original position in the number to achieve the normalized form. This count will determine the exponent of 10.
4. Apply the Power of 10: The normalized number is then multiplied by 10 raised to the power of the count from the previous step. If the original number was greater than 10, the exponent will be positive. If the original number was less than 1, the exponent will be negative.

Firstly, convert the number to a decimal with only one number before the decimal point by dividing by 10 as many times as needed e.g.

2345 ÷ 10 = 234.5 ÷ 10 = 23.45 ÷ 10 = 2.345

We divided it by 10 three times to get our decimal.

Now we can write our standard form:

2.345 x 10 to the power of 3 (because we must multiply the decimal by 10 three times)

If we have a very small number, we multiply it to get a standard decimal e.g.

0.00071 x 10 = 0.0071 x 10 = 0.071 x 10 = 0.71 x 10 = 7.1

We multiplied by 10 four times.

When it comes to writing the number in standard form, we always use multiplication, so when we have multiplied to reach the decimal, we have to multiply it by a negative number:

7.1 x -10 to the power of 4

Hi Ella! To write numbers in standard form, we have to write it in the form of A x 10^n

So the 3 rules are as follows:

1. A must be 1 or more and less than 10.
2. A must be multiplied by 10 to the power of some number (n)
3. n must be a whole number

Here is an example: Write 3420 in standard form

• A = 3.42 because that is between 1 and 10
• Looking at our value for A we can work out what n must be. We want to go from 3.42 to 3420. Imagine 3420 is written as 3420.0. Look at where the decimal point is. Count how many times we move the decimal point to get from 3.42 to 3420.0
• This means that n is 3.
• Bring this all together and we have an answer of 3420 = 3.42 x 10^3

I hope this helps! :)

if written in the from Y*10^n, the 3 rules are :

1: Y must be between 1 and 10

2: standard form uses base 10 (10 to the power of something)

3: n must be a whole number

A must be greater than 1, less than 10. A must be multiplied by 10 to the power of a number (n). n must be a whole number.

The first number has to be between 1 and 10 but less than 10

It is always x 10 to the power of n

n has to be an integer

1.It should be in the form of Ax+By=C

2.A,B, and C must be integers

3.A cannot be zero