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!

The three rules for writing numbers in standard form are:

1. Write the significant digits followed by the appropriate power of 10.

2. The significant digits should be between 1 and 10.

3. The power of 10 indicates the magnitude or scale of the number.

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 :)

A must be 1 or more and less than 10.

A must be multiplied by 10 to the power of some number (n)

n must be a whole number.

a x 10^n, 1=< a <10, n is Z

a x 10^n, 1=<a <10 n is Z

a x 10^n, 1=< a< 10 , n is Z

1) The number X must be between 1.0 to 9.9 (An infinite number), and power Y must be an integer

2) The format must be X * 10^Y

3) The power Y = the number of digits between the decimal point and number X.

E.g., 819,000,000

The number is 8.19, and there are 8 digits. 8.19 * 10^8

The standard form looks like 1.27 x 10³ for example which equates to 1270.

The idea behind this is to make numbers easy to see and removes the need to write a lot of zeros which can be hard to read.

Firstly, in the example, I would have the number 1270. I place a decimal point after the first number making it 1.270 and then I count the number of digits after the 1. In this case, there are three which makes the standard form answer: 1.27 x 10³

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❌