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

A number is in standard form when it’s of the form:

a x 10^b where,

a is between 1 and 10 (inclusive of 1 but not 10), and b is an integer.

The a part is usually quite easily determined, however, the b part must be taken care of when converting ordinary numbers to standard form. Count how many spaces the decimal point has moved across to figure out the correct power of 10.

For example,

543,000 in standard form is 5.43 x 10^5.

0.00000678 in standard form is 6.78 x 10^-6.

Standard form is a way to write large, or small numbers. It takes a standard format (hence the name) of *.*** x 10^* so

3000 is written as 3 x 10^3

0.00045 is written as 4.5 x 10^-4

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

2.A,B, and C must be integers

3.A cannot be zero

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. 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

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!

1. The coefficient must be between 1-10 ( can be equal to 1, but less than 10 )
2. The number is multiplied by 10
3. The exponent of 10 indicates the direction and size of shift

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 :)

In standard form, numbers are written in the following way:

Rule 1] A × 10^n

Rule 2] 'A' can be any number between 1 and 10, but not 10 itself.

Rule 3] 'n' can be any integer.

Example:

250

250 = 2.5 × 100 = 2.5 × 10^2

[ Explanation: Here the number 250 is written in the form A × 10^n

where A = 2.5, which is between 1 and 10 but not 10 itself

n = 2, which is an integer]

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.

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

Only one digit before the decimal point.

You need x10 to the power something.

The power is how many times you move the decimal point to get back to the original number.

The steps to writing a number in standard form are:

• Step 1: The first part must be a number between 1 and 10 (1 or bigger and less than 10). So it needs to be 1 or bigger and smaller than 10.
• Step 2: The second part must be a power of 10. This tells us how many times we need to multiply or divide the first part by 10 to get the ordinary number.
• Step 3: The power of the 10 is positive for big numbers and negative for small numbers

In standard form, the first number must be between 1 and 10, for very large numbers you multiply the first number by 10 raised to the power of a positive number, for tiny numbers you multiply the first number by 10 raised to the power of negative number.

If written in the form Y x 10^n, the 3 rules are:

1) Y must be between 1 and 10 (greater than or equal to 1 but less than 10)

2) standard form uses base 10, I.e. 10 to the power of something (n)

3) n must be a whole number.

Example:

3.5 x 10^3✅

0.4 x 10^3❌