Power of 10

Introduction to Power of 10

The power of ten, in maths, any of the integer (whole-valued) exponents of the number 10. A power of 10 is as many number 10s as designated by the exponent multiplied together. Therefore, shown in long-form, a power of ten is the number 1 subsequent to n zeros, in which ‘n’ is the exponent and is greater than 0; for example, 106 is mathematically written as 1,000,000. When n is less than 0, the power of 10 is the number 1 n places followed by the decimal point; for example, 10−3 is written 0.001.



Power of 10 to Zero

When n equals to 0, the power of 10 will be 1; i.e., 100 = 1. Refer to the below table for expressions in positives and negative powers of 10.


Powers of 10

101 = 10

100 = 1

102 = 100

10-1 = 0.1

103 = 1000

10-2 = 0.01

104 = 10,000

10-3 = 0.001

105 = 100,000

(one hundred thousand)

10-4 = 0.0001

(one ten thousandth)

106 = 1,000,000

(one million)

10-5 = 0.00001

(one hundred thousandth)

107 = 10,000,000

(ten million)

10-6 = 0.000001

(one millionth)

108 = 100,000,000

(one hundred million)

10-7 = 0.0000001

(one ten millionth)

109 = 1,000,000,000

(one billion)

10-8 = 0.00000001

(one hundred millionth)

1010 (10 to the tenth power) = 10,000,000,000

(ten billion)

10-9 = 0.000000001

(one billionth)


Multiplying and Dividing Powers of 10

Maybe you're not sure that it's useful to be able to write numbers in powers of ten math or mega 10 powers. Well, powers of ten maths are quite helpful when performing math calculations, as well. Let's say if we ask you ''what are 10 times 1,000?'' Hardly anything- it's just 10,000. But what if we ask ''what will be one trillion times one quadrillion?''

It concludes that the multiplication of really large numbers is easy with powers of ten. All you need to do is to add up the exponents, and you're sorted. Let's consider the example we just quoted above. What is one trillion times one quadrillion? First, one trillion is 1012, and one quadrillion is 1015. So the correct answer is 1027, which is a huge number. Now, you can see that almost immediately, without requiring a calculator, we did it shorthand.


Power of Ten Prefixes

When a numerical digit represents a quantity instead of a count, SI prefixes can be used - therefore "femtosecond", not "one quadrillionth of a second'' - although most frequently powers of 10 are used rather than some of the very low and very high prefixes. In certain cases, specialized units are taken help of, such as the light-year particle physicists barn or the astronomer's parsec.

Nonetheless, large numbers carry an intellectual intrigue and are of mathematical interest, and assigning them names is one of the ways in which most of us try to conceptualize and understand them.


Solved Examples

Solve the following expressions:

Log (106) = 6

Log (1027) = 27

Log (10365.2748) = 365.2748

Log (10-5) = -5

Log (x) -5 → x = 105

Log (x) = 6.789 → x = 106.789

Log (x) = -2.23 → x = 10-2.23


Fun Facts

  • The power of 10 is easy to remember since we use base 10 of a number system.

  • For 10n having ‘n’ a positive integer, just write "1" with n zeros after it. For negative powers 10−n, write “0" followed by n−1 zeros, and then a 1. The powers of 10 are extensively used in scientific notation.

FAQs (Frequently Asked Questions)

Q1. What is Meant by Logarithm?

Answer: Logarithm, the power or exponent to which a base should be raised to produce a given number. Written mathematically, x is the logarithm of n to the base b if bx = n, where case one writes x = logb n. For example, 24 = 16; thus, 4 is the logarithm of 16 to base 2, or 4 = log2 16. Similarly, since 103 = 1000, then 3 = log10 1000. Logarithms of the second-mentioned sort (that is, logarithms with base 10) are known as common, or Briggsian, logarithms and are simply written log n.

Q2. What is the importance of ‘logs’ in powers?

Answer: Are you assuming if there's an opposite to powers of 10? Something like how multiplication is the opposite of division or addition is the opposite of subtraction. It appears that there is such a thing called: ``logs'' or “logarithms”. Logs initially emerged to be important for multiplying and dividing and were used all the time in performing arithmetic operations with the help of slide rules. Now that calculators are commonplace, the use of logarithms for fundamental calculations is steadily disappearing, but it can still be worthwhile. And while employing logarithms for simple arithmetic calculations is not so common, there are other uses for logarithms in many areas of science.