Converting from standard form

Find the refreshed revision resources for GCSE Maths: Converting from standard form, with step-by-step slideshows, quizzes, practice exam questions, and more!

To convert a number in standard form to an ordinary number, simply do the multiplication.

Examples

\(1.34 \times 10^3\) is 1,340, since \(1.34 \times 10 \times 10 \times 10 = 1,340\).

\(4.78 \times 10^{-3}\) is 0.00478, as \(4.78 \times 0.001 = 0.00478\).

Question

Write the following as ordinary numbers:

\(2.99 \times 10^7\)
\(1.36 \times 10^{-7}\)

This process can also be sped up by considering where the first digit is compared to the units column.

Examples

\(3.51 \times 10^5\) = 351,000 because the 3 moves 5 places away from the units column. Two places are filled by 5 and 1. Put zeros in the other three places.

\(3.08 \times 10^{-4}\) = 0.000308 because the 3 moves 4 places away from the units column. Put zeros in the other 3 places. Focus on the 3, not the 8.

Question

Complete the table with the measurements in standard form.

Example	Number (metres)	Standard form
Height of a skyscraper	300
Length of a virus	0.0000003
Size of a galaxy	300,000,000,000,000,000,000
Height of a mountain	3,000
Nucleus of an atom	0.00000000000003

Example	Height of a skyscraper
Number (metres)	300
Standard form

Example	Length of a virus
Number (metres)	0.0000003
Standard form

Example	Size of a galaxy
Number (metres)	300,000,000,000,000,000,000
Standard form

Example	Height of a mountain
Number (metres)	3,000
Standard form

Example	Nucleus of an atom
Number (metres)	0.00000000000003
Standard form

Example	Number (metres)	Standard form
Height of a skyscraper	300	\(3 \times 10^2~\text{m}\)
Length of a virus	0.0000003	\(3 \times 10^{-7}~\text{m}\)
Size of a galaxy	300,000,000,000,000,000,000	\(3 \times 10^{20}~\text{m}\)
Height of a mountain	3,000	\(3 \times 10^3~\text{m}\)
Nucleus of an atom	0.00000000000003	\(3 \times 10^{-14}~\text{m}\)

Example	Height of a skyscraper
Number (metres)	300
Standard form	\(3 \times 10^2~\text{m}\)

Example	Length of a virus
Number (metres)	0.0000003
Standard form	\(3 \times 10^{-7}~\text{m}\)

Example	Size of a galaxy
Number (metres)	300,000,000,000,000,000,000
Standard form	\(3 \times 10^{20}~\text{m}\)

Example	Height of a mountain
Number (metres)	3,000
Standard form	\(3 \times 10^3~\text{m}\)

Example	Nucleus of an atom
Number (metres)	0.00000000000003
Standard form	\(3 \times 10^{-14}~\text{m}\)

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Standard form - OCRConverting from standard form