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

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

1. The first number must be between 1 and 10
2. Next write x10
3. Finally, write in the correct power. If the number you are converting was a decimal, then it is likely that your power will need to start with a minus in front. However, if the number is an integer, your power will be positive.

Standard form takes general formula of M x Y^n

• The first rule is that the M must be a number from 1 to 10 (equal to or greater than 1 but less than 10).
• The second rule is that Y takes a number of 10 ( This is also know as a base of 10, 10 to the power).
• The 3rd and final step is n must be a whole number.

For example: 4 x 10^3 = 4x1000=4000

If M is not a whole number then you must use a extra step (times the decimal by 10 to get a whole number between 1-10), i.e. 0.5 x10^4 = 5 times 10^3, this reduces power by 1 since you multiplied by 10.

If a number is greater than 10 you divide by 10 increasing power by 1.

i.e. 50 x 10^4= 5x10^5

• Step One: Create the Base Number
• Step Two: Set the Base Multiplied by a Multiple of Ten
• Step Three: Converting the Multiple of Ten to an Exponent

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.

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

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

Standard Form is written in the form a x 10^n, where a is between 1 and 10 (greater than or equal to 1 but less than 10) and where n must be a whole number (positive or negative).

Example:

Correct: 3.5 x 10^3 or 2 x 10^-6

Wrong 0.3 x 10^2 or 13.4 x 10^5

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 of writing down very large or very small numbers easily. 10 to the power of 3 = 1000, so as 4 × 10 to the power of 3 = 4000.

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

For example, take the number 123000000, an easier way of writing this number is ​​

1.23 × 108.

Here are the three simple rules for writing numbers in standard form:

1. Move the decimal point so the number is between 1 and 10.
2. Multiply by 10 raised to the power of how many places you moved the decimal.
3. Use a positive exponent for large numbers (greater than 10) and a negative exponent for small numbers (less than 1).

Examples:

1. 3,600 → 3.6 × 10³
2. 0.052 → 5.2 × 10⁻²
3. 89,000,000 → 8.9 × 10⁷

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

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! :)

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