The idea behind standard form is to write both very large and very small numbers in a convenient form. Here are a couple of examples of numbers written in standard form:
In this tutorial we learn how to write numbers in standard form. We do so by writing the three numbers:
When we write a number in standard form, we must write it in yje following way: \[a \times 10^k\] where the following two conditions must be met:
Write each of the following numbers in standard form:
We find the following results:
When writing numbers in standard form, we usually round numbers to two or three significant figures. For instance, consider the number: \[2 \ 347 \ 128\] Without any rounding, writing this in standard form, leads to: \[2.347128\times 10^6\] This notation isn't practical. Instead, when writing numbers in standard form, we usually round to 2 or 3 significant figures, so that \(2.347128\times 10^6\) becomes:
Writing all of your answers to three significant figures, write each of the following in standard form:
We find the following results:
Although some calculators can present results in standard form, many use a slightly different notation to the one we have see here.
Calculators replace the number \(10\) by the letter \(E\)
Here are some examples of what a calculator can display and the number, in standard form, they are referring to.
With your calculator, try calculating: \[987,654,321 \times 123,456,789\] You're likely to find: \[1.21933\text{E}17\] This means: \[1.21933\times 10^{17}\]
Notice that we had to convert the number in decimal form, via:
With your calculator, try calculating: \[5 \div 1234567890\] You're likely to see a result looking like: \[4.05\text{E}-9\] This means: \[4.05\times 10^{-9}\]
Notice that we had to convert the number in decimal form, via:
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