The negative powers of 10 are expressed in a different way. Similarly, we have some specific names for some positive powers of 10 which are given in the following table. For example, 10 6 (10 to the power of 6) is known as a 'million' and the SI prefix of 10 power 6 is 'giga' which is represented by the SI symbol G. The powers of 10 have some specific names (though not all powers) for some specific powers. The following table shows the powers of 10 chart which includes positive powers and negative powers. And if we write it in the form of a fraction it will be 1/100000. Now, the value of 10 -5 in the decimal form will be 0.00001. Similarly, if we write 10 -5 in the expanded form, it will be 10 -5 = 1/(10 × 10 × 10 × 10 × 10). And if we write it in the form of a fraction it will be 100000/1. Now, the value of 10 5 in the decimal form will be 100000. For example, if we write 10 5 in the expanded form, it will be 10 5 = 10 × 10 × 10 × 10 × 10. The powers of 10 chart shows that the different powers of 10 have different values. Here, we placed 5 zeros after the decimal point (followed by 1) as the power was a negative 6 and 6 - 1 = 5.
When the power is negative, 10 -x = '0 point followed by (x -1) number of zeros followed by 1".įor example, 10 -6 = 0.000001.Here, there are 6 zeros placed after 1 because the power of 10 is 6. When the power is positive, 10 x = '1 followed by x number of zeros'.įor example, 10 6 = 1,000,000.By using these two examples, we can conclude two things that are very useful to calculate the powers of 10. If x is negative, then we apply the property of exponents, a -m = 1/a m and then we apply the same logic as explained earlier. If x is positive, we simplify 10 x by multiplying 10 by itself x times. The powers of 10 are of the form 10 x, where x is an integer. This means that we need to multiply 10 seven times, that is, 10 7 = 10 × 10 × 10 × 10 × 10 × 10 × 10 For example, 10 to the 7th power means 10 7. Now, let us try to understand it the other way round. Here, 10 is the base and 9 is the power and this is read as 10 to the ninth power. Therefore, exponents help to express this easily and this value (10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1000000000) can be expressed as 10 9. Now, if we need to multiply 10 thirty times, it would be even more difficult to write the product with so many zeros. If we multiply 10 a couple of times it becomes difficult to write the number as in this case, 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 1000000000. These numbers which are written as exponents are the powers of 10. The powers of 10 means when 10 is multiplied a certain number of times, the product can be expressed using exponents.
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