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Scientific Notation Formula

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In mathematics, there is a plethora of numerals and numerical figures. We are all familiar with the concept of the number line and also that it extends infinitely to the left as well the right of zero. As a result, the numbers keep on becoming smaller and smaller (towards the left) or bigger and bigger (towards the right) to the point where it is no longer convenient for them to be expressed in decimal form. This is where the concept of scientific notation comes into the picture. It is discussed below.

What is Scientific Notation?

Scientific notation is a method of displaying extremely big or extremely small numbers in a more straightforward manner. As discussed above, numbers can be extended indefinitely, but such large numbers cannot be written on a sheet of paper. In addition, the numbers in the millions place after the decimal are required to be represented in a more straightforward manner. As a result, representing a few integers in their expanded form is challenging. As a result, we employ scientific notation.

Simply stated, scientific notation is employed to express any number as a decimal number with its value between 1 and 10, excluding 10 multiplied by a power of 10. The general form of a scientific notation is:

n × 10m

where,

n is a real number such that 1 ≤ n < 10 and is known as the significant.

Rules of Scientific Notation

  • The scientific notation is divided into two parts: the first is merely the digits, with the decimal point after the first digit, and the second is multiplication with 10 to a power number of decimal point, which places the decimal point where it belongs.
  • The decimal point must move to the left if the given number is higher than 1 and multiples of 10, and the power of 10 will be positive.

Example: Write 5890000 in scientific notation.

Solution: 

Clearly the given number has only 3 considerable numbers/ figures since the zeroes are to be regarded as mere placeholders.

Following the first rule of scientific notation, put a decimal after the first digit in the given number.

5890000 = 5.89 × 100 × 10000

= 5.89 × 106

Similar Problems

Question 1. Write 897,000,000,000 in scientific notation.

Solution:

Clearly the given number has only 3 considerable numbers/ figures since the zeroes are to be regarded as mere placeholders.

Following the first rule of scientific notation, put a decimal after the first digit in the given number.

897,000,000,000 = 8.97 × 100 × 1000000000

= 8.97 × 102 × 109

= 8.97 × 1011

Question 2. Write 990000000000 in scientific notation.

Solution:

Clearly the given number has only 3 considerable numbers/ figures since the zeroes are to be regarded as mere placeholders.

Following the first rule of scientific notation, put a decimal after the first digit in the given number.

990000000000 = 9.9 × 10 × 10000000000

= 9.9 × 101 × 1010

= 9.9 × 1011

Question 3. Write 0.00000077 in scientific notation.

Solution:

Move the decimal point up to 7 positions to the right of 0.00000077.

To make the number 7.7, the decimal point was moved 7 places to the right.

The decimal is moved to the right since the numbers are fewer than ten. As a result, we employ a negative exponent in this case.

⇒ 0.00000077 = 7.7 × 10-7

Question 4. Write 0.0000426 in scientific notation.

Solution:

Move the decimal point up to 5 positions to the right of 0.0000426.

To make the number 4.26, the decimal point was moved 5 places to the right.

The decimal is moved to the right since the numbers are fewer than ten. As a result, we employ a negative exponent in this case.

⇒ 0.0000426 = 7.7 × 10-5

Question 5. Write 699000000 in scientific notation.

Solution:

Clearly the given number has only 3 considerable numbers/ figures since the zeroes are to be regarded as mere placeholders.

Following the first rule of scientific notation, put a decimal after the first digit in the given number.

699000000 = 6.99 × 100 × 1000000

= 6.99 × 102 × 106

⇒ 699000000 = 6.99 × 108

Question 6. Write 358000000 in scientific notation.

Solution:

Clearly the given number has only 3 considerable numbers/ figures since the zeroes are to be regarded as mere placeholders.

Following the first rule of scientific notation, put a decimal after the first digit in the given number.

358000000 = 6.99 × 100 × 1000000

= 3.58 × 102 × 106

⇒ 358000000 = 3.58 × 108

Question 7. Convert 0.00000055 into scientific notation.

Solution:

Move the decimal point up to 7 positions to the right of 0.00000055.

To make the number 5.5, the decimal point was moved 7 places to the right.

The decimal is moved to the right since the numbers are fewer than ten. As a result, we employ a negative exponent in this case.

⇒ 0.00000055 = 5.5 × 10-7


Last Updated : 24 Jan, 2024
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