## Powers of 10 exponents

**Introduction :**

How to calculate powers of 10 with positive and negative exponent ?

Let us learn how to represent 10 power any exponents and which is the base and which is the exponent.

10 power n can be represented as 10n. 10 is the base. n is the exponent. An exponent says how many times the base number has to multiplied.

Consider 103.Here 10 is the base and 3 is the exponent. So exponent 3 says that the number 10 has to be multiplied thrice. So 103 = 10 x 10 x 10 = 1000

103 could be read as 10 to the power 3 or 10 cube or 10 to the third power.

Learning powers of 10 with positive exponents:

Consider 10 4

104 = 10 x 10 x 10 x 10 = 10000

104 could be read as 10 to the power 4 or 10 to the fourth power.

It is very useful to learn powers of 10. We could write very large numbers using powers of 10. Scientists and engineers make use of this powers of 10 to represent very large and small numbers.

Consider 70000. It has 4 zeros. So we could write 70000 as 7 x 104

Consider 135000000. It has 6 zeros. So we could write this as 135 x 106.Otherwise 1.35 x 108. Since we are keeping the decimal point after the first number and two more numbers are after decimal we could add 2 to the power 6.So, we could write 135000000 as 1.35 x 108.

The method which we are using is called scientific notation or standard form.

The simplest way is keep the decimal point after the first number and write the significant digits after it and then write x 10. Then count the number of digits after the first number and write it as the power of 10.

Let us try some more examples:

Examples:124000 = 1.24 x 105

We had kept a decimal point after the first number 1 and we had written the significant digits 2 and 4 after the decimal point. Count the number of digits after the first number. It is 5. So write 5 as the power of 10.

5900000000000 = 5.9 x 1012

We had kept a decimal point after the first number 5. Write the significant digit 9 after the decimal point and count the number of digits after the first number. It is 12. So write 12 as the power of 10.

Learning powers of 10 with negative exponents:

Very small numbers can also be written in powers of ten notation, but small numbers use negative exponents. For example, 0.001 = 10-3. What is the need to put the negative sign? We know that 0.001 can be written as 1/1000 = 1/103. Then it becomes clear that the negative power simply indicates the power of ten of the denominator when you have written the number as a fraction.

**Note: To write the powers of 10 for small numbers, count the zeros after the decimal and add one.**

Example:

0.1 = 1 x 10-1

0.01 = 1 x 10-2

0.0001 = 1 x 10-4