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

1 year ago

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40 Replies

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6007 views

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Ella Schimmel

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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

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Maddie H Verified Sherpa Tutor ✓

18 years exp. QTS KS1-5 SATS GCSE A-Level SENDMH - fun-loving teacher

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

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 :)

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N
Natasha Leah

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!

S
Sarah K

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.
E
Emma Thomas

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.

I
Ikrah

then you need to multiply by 10

write together

A

1. Moving the decimal point to the back of the first non-European number

2.Countiting the number of steps of shifting the decimal point to the back of the first non-zero number which will form the exponent on the 10.

3. Inclusion of X10 raise to n. Where the n is the number of steps of shifting of the decimal point to the back of the first non-zero number.

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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

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I
Ify Godwin

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.

V
Vicky Miller

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

Lucie-Grace R Verified Sherpa Tutor ✓

Maths Initial Teacher Trainee

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! :)

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A
Ana Obreajan

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

L
Lillie Smith

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.

I
Ian Mclachlan

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

N
Nazneen

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

2.A,B, and C must be integers

3.A cannot be zero

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