˿

Standard form – WJECConverting into standard form and ordinary numbers

Performing calculations with very big or small numbers can be difficult. Such calculations, for example those related to space, can be made easier by converting numbers in and out of standard form.

Part of MathsNumber

Converting between ordinary numbers and standard form

To convert a number into , split the number into two parts - a number multiplied by a power of 10.

Large numbers

Example

Write 50,000 in standard form.

50,000 can be written as: \(5 \times 10,000\)

\(10,000 = 10 \times 10 \times 10 \times 10 = 10^4\)

So \(50,000 = 5 \times 10^4\)

Question

What is 800,000 written in standard form?

So, \(34 \times 10^7\) is not in standard form as the first number is not between 1 and 10. To correct this, divide 34 by 10. To balance out the division of 10, multiply the second part by 10, which gives 108.

\(34 \times 10^7\) and \(3.4 \times 10^8\) are identical but only the second is written in standard form.

Example

What is 87,000 in standard form?

87,000 can be written as \(8.7 \times 10,000\)

\(10,000 = 10 \times 10 \times 10 \times 10 = 10^4\)

So \(87,000 = 8.7 \times 10^4\)

Question

What is 135,000 in standard form?

Example

3,000,000 = \(3 \times 10^6\) because the 3 is 6 places away from the units column.

36,000 = \(3.6 \times 10^4\) because the 3 is 4 places away from the units column.

Question

What is 103,000,000 in standard form?

Question

What is 1,230 in standard form?