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Standard Form: Conversion

Converting Normal Numbers to Standard Form

To convert large normal numbers to standard form you have to put a decimal point after the first digit and ignore the zeros at the end (if there is another number that is not 0 after the zero(s), don’t ignore them). In the example on the right you should end up with 3.844. Then, you have to count the digits from the right to the left until you reach your decimal point. In the example, there are 8 digits on the right side of the decimal point. This will be your power. When you write down the answer, you will get                        . The 3.844 being the decimal we calculated earlier and the 8 being the number of digits to the decimal point. To convert small normal numbers into standard form, you have to find the first non 0 digit after the decimal point. After this digit, you place your new decimal point ignoring everything that is in front of this digit. In the example on the right, the digit would be 5 and the decimal would be 5.67. The only thing that you have to do now is to count how many digits there are between the original decimal point and the new (imaginary one). In this case, there are 9 digits so the final answer would be                      . here are a couple of examples to outline this. Some calculators have settings that allow you to display solutions in standard from. If you have access to a calculator like this, you can convert into standard form by just typing in the normal number (small or large). If your number is 374000000 your calculator will show you something like this 3.74 e8. The e stands for 10 to the power of. To check if your calculator supports this function, look on the developers website or in the manual or ask your maths teacher. Converting Standard Form to Normal Numbers Converting standard to normal numbers is a lot easier than doing it the other way around. There are two methods depending on the resources available: 1. The Calculator Method If you have access to a calculator, you can convert standard form into normal numbers just by simply typing in the standard form version. The answer shown will be the normal number. (This works with large and small standard form numbers). 2. The Written/Mental Method If you do not have a calculator or you are not allowed to use one you can use this method. If you are dealing with a large number in standard form, just move all numbers to the left (leaving the decimal point stationary) by the number of places indicated by the power. So if the power is 6, you move all numbers to the left by six places. At the end, you should normally be able to remove the decimal point as there will probably only be zeros. If you are dealing with a small number, just move all the digits right by the number of decimal places indicated by the power. So if the power is 9, move each digit 9 decimal places to the right. Moving on to Some Calculations Now that you know how to convert standard form into normal numbers and vice versa, you can try to do some calculations with numbers in standard form. If you haven’t looked at the standard form introduction, make sure to check it out as maths will not be the only subject that you might meet standard form in. Please share this page if you like it or found it helpful!
Example 1 In this example, the decimal is 3.45 and there are 9 digits after the imaginary decimal point so the power will be 9.
Example 2 In this example, the decimal is 4.9 and there are 8 digits after the imaginary decimal point so the power will be 8.
Example 1 In this example, the first non 0 digit after the decimal point is 3 so the decimal becomes 3.75. There are 6 digits between the original and the new decimal point so the power is -6.
Example 2 In this example, the first non 0 digit after the decimal point is 8 so the decimal becomes 8.92 There are 7 digits between the original and the new decimal point so the power is -7.
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Standard Form - Calculations
6.0 STANDARD FORM 6.2 STANDARD FORM: CALCULATIONS
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Chapter 6.1:  Learning Outcomes Students will know how to convert from normal numbers to standard form! Students will know how to convert from standard form to normal numbers with and without a calculator!
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