Standard Form

We usually write very small numbers or very large numbers in standard form. To write a number in standard form, we write it as A\times 10^{ n }, where A\geq 1 but <10.

So, 1\le A<10

and n is an integer.

For example, the speed of light is 299,793kms^{-1}. In standard form, this is 2.99793\times 10^{5} kms^{-1} or 3\times 10^{5} kms^{-1} in standard form, correct to three significant figures.

Let’s look at some more examples:

Example

Rewrite in standard form:
a) 125600000000

*** QuickLaTeX cannot compile formula:
</span><strong><span class="has-inline-color has-vivid-green-cyan-color">b) </span></strong><span class="has-inline-color has-black-color">1300 </span><span class="has-inline-color has-vivid-green-cyan-color">c)</span><span class="has-inline-color has-black-color"> 0.000001256 </span><strong><span class="has-inline-color has-vivid-green-cyan-color">d)</span></strong><span class="has-inline-color has-black-color"> 0.00013</span>
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<strong><span class="has-inline-color has-vivid-green-cyan-color">a)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.

125,600,000,000=1.256\times 10^{ 11 }</span><strong><span class="has-inline-color has-vivid-green-cyan-color">b)</span></strong><span class="has-inline-color has-black-color">13,000=1.3\times 10^{ 4 }</span><strong><span class="has-inline-color has-vivid-green-cyan-color">c)</span></strong><span class="has-inline-color has-black-color">0.000001256=1.256\times 10^{ -6 }</span><strong><span class="has-inline-color has-vivid-green-cyan-color">d)</span></strong><span class="has-inline-color has-black-color">0.0013=1.3\times 10^{ -4 }
*** QuickLaTeX cannot compile formula:
</span>
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<span class="has-inline-color has-black-color">In the above,

*** Error message:
Missing $ inserted.

Ais a number such that1\le A<10and the indexnis an integer.Large numbers greater than10will havenpositive as in a) and b) and small numbers less than1will haven
*** QuickLaTeX cannot compile formula:
negative as in c) and d).</span>
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<h2 id="h-example-1"><span class="has-inline-color has-luminous-vivid-orange-color">Example</span></h2>
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Write down the following numbers in standard form:
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<strong><span class="has-inline-color has-vivid-green-cyan-color">i)</span></strong> 14500000
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<strong><span class="has-inline-color has-vivid-green-cyan-color">ii)</span></strong> 0.00000145
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<strong><span class="has-inline-color has-vivid-green-cyan-color">iii)</span></strong> 145
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<strong><span class="has-inline-color has-vivid-green-cyan-color">iv) </span></strong>14.5
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<strong><span class="has-inline-color has-vivid-green-cyan-color">v)</span></strong> 0.145
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In standard form, these are:
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<strong><span class="has-inline-color has-vivid-green-cyan-color">i)</span></strong>

*** Error message:
Missing $ inserted.

1.45\times 10^{7}
*** QuickLaTeX cannot compile formula:

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<strong><span class="has-inline-color has-vivid-green-cyan-color">ii)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.

1.45\times 10^{-6}
*** QuickLaTeX cannot compile formula:
</span>
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<strong><span class="has-inline-color has-vivid-green-cyan-color">iii)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.

1.45\times 10^{2}
*** QuickLaTeX cannot compile formula:
</span>
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<strong><span class="has-inline-color has-vivid-green-cyan-color">iv)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.

1.45\times 10
*** QuickLaTeX cannot compile formula:
</span>
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<strong><span class="has-inline-color has-vivid-green-cyan-color">v)</span></strong><span class="has-inline-color has-black-color">

*** Error message:
Missing $ inserted.

1.45\times 10^{-1}$