Converting to & from Standard Form (Edexcel IGCSE Maths)

Spec point — 1.9A

Converting to and from standard form

What is standard form and why is it used?

• Standard form is a way of writing numbers using powers of 10

• It is helpful to see the size of very large and very small numbers

• This allows us to:

  • Write them more concisely
  • Compare them more easily
  • Perform calculations with them more easily

How do I write a number in standard form?

• Numbers written in standard form are always written as:

$a\times10^{n}$

• Where:

  • $1\leq a<10$ ($a$ is bigger than or equal to 1 and less than 10)

  • $n$ is an integer

    • $n<0$ ($n$ is negative) for numbers bigger than 0 and less than 1
    • $n=0$ for numbers bigger than or equal to 1 and less than 10
    • $n>0$ ($n$ is positive) for numbers bigger than or equal to 10

How do I write a large number in standard form?

• To write a large number such as 32 400 in standard form

  • Identify the value of $a$

    • 3.24

  • Find how many times you must multiply 3.24 by 10, to make 32 400

    • Count how many places you need to move the digits
    • We need to multiply by 10 four times

  • 32 400 = 3.24 × 10 × 10 × 10 × 10 = 3.24 × 10⁴

How do I write a small number in standard form?

• To write a small number such as 0.0000324 in standard form

  • Identify the value of $a$

    • 3.24

  • Find how many times you must divide 3.24 by 10, to make 0.0000324

    • Count how many places you need to move the digits
    • We need to divide by 10 five times
    • We are dividing rather than multiplying so the power will be negative

  • 0.0000324 = 3.24 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 3.24 × 10^-5

Exam Hint On some calculators, typing in a very large or very small number and pressing $\boxed{=}$ will convert it to standard form.

Worked Example (a) Without a calculator, write 0.007052 in standard form.

Answer:

Standard form will be written as a × 10ⁿ* where a is between 1 and 10* *Find the value for *a

a = 7.052*

The original number is smaller than 1 so n will be negative Count how many times you need to divide a by 10 to get the original number

0.007052 = 7.052 ÷ 10 ÷ 10 ÷ 10 (3 times)

Therefore n = -3.

Final answer: 0.007052 = 7.052 × 10**^-3

(b) Without a calculator, write 324 500 000 in standard form.

Answer:

Standard form will be written as a × 10ⁿ* where a is between 1 and 10* *Find the value for *a

a = 3.245*

The original number is larger than 1 so n will be positive Count how many times you need to multiply a by 10 to get the original number

324 500 000 = 3.245 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 (8 times)

Therefore n = 8

Final answer: 324 500 000 = 3.245 × 10**⁸