## Converting numbers to scientific notation and back to standard format

This article explains how to convert numbers to scientific notation and back again to standard format. It also contains two calculators that will enable calculations to be checked and that provide feedback on common data entry input errors.

## How do you convert numbers to scientific notation?

## How do you convert numbers in scientific notation back to decimals?

Above we have seen that numbers such as 6 x 10 ^{3 }or 3.5 x 10 ^{-1} are expressed in normalised scientific notation. How do you convert a number in scientific notation back to standard format again?

First we will define terms. Looking at 3.5 x 10 ^{-1}, you can see that we have a number, 3.5, multiplied by 10 (base) to the power of -1.

The number before 10 to the power of -1 is usually called the fractional coefficient and the -1 is referred to as the exponent.

In this case we must make the fractional coefficient smaller. So if you wish to convert 3.5 x 10 ^{-1} to a standard number simply move the decimal point to the left by one place; the exponent indicates the number of places to move the decimal point. So if the exponent was -4 you would move the decimal point 4 places.

Let’s look at what happens when the exponent is positive. In this case we are making the fractional coefficient larger and we will move the decimal point to the right. Again, the exponent indicates the number of places that the decimal point should be moved.

Converting numbers from one format to another can easily be done using spreadsheet programmes such as Numbers or Excel or the calculator below.

The figure below illustrates how you might set up an Excel spreadsheet to convert, say, 3.2×10 ^{-4 }which is in scientific notation^{ }to standard format. Prepare two columns, label one Fractional coefficient (A1) and the other Exponent of base 10 (B1). The fractional coefficient is then entered at A2 and the exponent, in this case -4, entered into cell B2. The result of the calculation 0.00032 is given in cell, B3.

To make the conversion, 3.2 is multiplied by 10^-4 as shown in the figure below. Hence =B2*10^B2 is entered into B3.