How do you express large numbers?

Exponents and powers are a method to express repeated multiplication of the same number. For eg- 8 × 8 × 8 can be written as 8³ where 8 is the base and 3 is the exponent. It is most commonly used to express the powers of 10 to write a very large number in a convenient manner. For eg- 100000 can be written as 10⁵.

Laws of Exponents

• To multiply two exponential numbers with the same bases, the exponents are added and the base remains the same. For eg- a^m × aⁿ = a^m+n.
• When the exponent has another exponent, the base remains the same but the powers are multiplied. For eg- (a^m)ⁿ = a^m×n.
• To divide two exponential numbers with the same bases, the exponents are subtracted and the base remains the same. For eg- a^m/aⁿ = a^m-n.

What is a Power Notation?

Power notation is a method to express numbers that are very large or very small. For eg- 1000000000000 can be written as 10¹² and 0.00000026 can be written as 2.6 × 10^-7. Scientific notation is a similar method to express numbers in the form of nth power of 10. For eg; 1.67 × 10⁷. 

Rules followed while writing a number into its power notation:

• The base of the power is always 10.
• The exponent may be positive or negative.
• The absolute value of the coefficient is greater or equal to 1 but less than 10.

Steps to express a large number:

Step 1: Write the given number.

Step 2: Count the number of digits.

Step 3: Place a decimal after one’s position.

Step 4: Multiply it by 10^n-1, where n is the number of digits of the number.

How do you express large numbers?

Solution:

Power notation is used to express very large numbers. Large number are converted into the form of coefficient time nth power of 10 following some certain rules. 

The rules are as follows:

• The base of the power is always 10.
• The exponent may be positive or negative.
• The absolute value of the coefficient is greater or equal to 1 but less than 10.

For eg: 16700000000 is written as 1.67 × 10¹⁰, 1500000000000 is written as 1.5 × 10¹² etc.

Similar Questions

Question 1: Write 1780000 in power notation?

Solution:

Given that the number is 1780000.

The total number of digits are 6.

Place the decimal after ones digit and write in the power of 10.

1780000 = 1.78 × 10⁶

Hence, the power notation of 1780000 is 1.78 × 10⁶.

Question 2: Write 9860000000000 in power notation?

Solution:

Given that the number is 9860000000000.

The number of digits are 12.

Place the decimal after ones digit and write in the power of 10.

9860000000000 = 9.86 × 10¹²

Hence, the power notation of 9860000000000 is 9.86 × 10¹².