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Explanation of Exponents to the Power of 10 - Succeed in Algebra. Also refer to multiples, large, small, numbers, mathematics, math, maths, Ron Kurtus, School for Champions. Copyright © Restrictions Exponents to the Power of 10by Ron Kurtus (10 January 2008) You can denote multiples of 10 as a power of 10. You can also
denote multiples of 1/10 as powers of 10. This leads to a convenient
way to denote very large or very small numbers that include other digits
than 10. Calculators
often use a variation of denoting the power of 10. Questions you may have are:
This lesson will answer those questions. There is a mini-quiz near the end of the lesson. Large numbersLarge multiples of 10 numbers can be written in terms of powers of 10. For example
This is very convenient, because all you have to do is to add the number of zeros and use that as the exponent. The number 10,000,000,000,000 has thirteen zeros and thus equals 1013. Numbers smaller than 1Numbers smaller than 1 can be written in powers of 10 with a negative exponent, which means the reciprocal of the number. For example:
The easy way to figure it out is to count the number of placed to the right of the decimal point. Another example is 0.0001 = 10-4, since there are four places to the right of the decimal point. Other numbersOther large and small numbers can be written as powers of 10. Large numbersSince most large numbers have other digits involved, you can break the number into parts. For example, the distance from the Earth to the Sun is approximately 92,000,000 miles. You could re-write that number as 92*1000000 miles, which can be designated as 92*106 miles.
Likewise,
Small numbersYou can also denote number with other digits in powers of 10, such as
Following the convention for writing numbers to the power of 10, you should change 25*10-4 to 2.5*10*10-4 = 2.5*10-3. Calculator notationMost hand-held calculators denote raising to a power of 10 with an E (meaning exponential). In other words, on a calculator 9.2*107 might be displayed as 9.2E7. Likewise, 2.5*10-3 would display as 2.5E-3 on the calculator. SummaryYou can denote large numbers that are multiples of 10 as a powers, such as 1,000,000 - 106. You can also denote small numbers as multiples of 1/10 as powers of 10, such as 0.0001 = 10-4. This leads to a convenient way to denote very large or very small numbers that include other digits than 10, such as 1.3*104 to denote 13,000. Calculators often use the variation of denoting the power of 10, such as 2E3 to denote 2*103. Be clever in the way you do things ResourcesThe following resources provide information on this subject: WebsitesBooksMiscellaneousMini-quiz to check your understanding1. What is 251,000 in in powers of 10? 2. What is 62*0.001 in in powers of 10? 3. What is 3.14/10000 in in powers of 10? If you got all three correct, you are on your way to becoming a Champion in Algebra. If you had problems, you had better look over the material again. What do you think?Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. We will try to get back to you as soon as possible. Share linkFeel free to establish a link from your website to pages in this site. 
Or use our form to send this link to yourself or a friend. Students and researchersThe Web address of this page is Please include it as a reference in your report, document, or thesis. Where can you go from here?
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