How to Simplify numbers using Scientific Notation?

The exponent or power of a number represents the number of times the former has been multiplied by itself. For instance, if let a be any real number which is multiplied n times by itself, then the exponent or power of a would be n. The exponent of a is n, and the formula aⁿ is read as a raised to the power n. Exponents and powers are used to represent very large or very small numbers conveniently while studying number lines.

Scientific Notation

Scientific notation is a more easy way of presenting extremely large or extremely small numbers. Numbers can be expanded forever, as previously stated, but such enormous numbers cannot be written on a piece of paper. Furthermore, figures in the millions place after the decimal have to be represented in a more understandable way. As a result, it’s difficult to represent a few integers in their enlarged form. As a result, scientific notation is used.

Under scientific notation, any number is written such that its value lies between the numbers 1 and 10, not including 10 but including 1.

n × 10^m

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

Rules of Scientific Notation

• The starting point should always be ten.
• Make sure that the given exponent is a real number. It makes no difference whether it is positive or negative.
• The coefficient’s absolute value is more than or equal to one, but it should be less than ten.
• Coefficients can be either positive or negative values, as well as whole or decimal integers.
• The remainder of the number’s significant digits is carried by the mantissa.

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

Question 8: 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