Topic Details (Notes format)

How to Use Scientific Notation

Subject: Mathematics

Book: Maths Mastery

Scientific notation expresses very large or very small numbers in the form m × 10^n, where 1 ≤ m < 10 and n is an integer. For example, the speed of light (~300,000,000 m/s) becomes 3.0 × 10^8 m/s, and a cell’s diameter might be 2.5 × 10^–5 m. To convert a number into scientific notation, move the decimal point until only one nonzero digit appears to its left, counting the moves to determine the exponent sign and magnitude. This is widely used in physics, astronomy, and chemistry to handle extremes in scale. Proficiency with scientific notation is crucial in data science, engineering, and daily tasks like reading a phone’s internal storage capacity or analyzing financial statements.

Practice Questions

The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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What is the cube of 4?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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If x^2 - 6x + 9 = 0, what is the value of x?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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If the sum of three consecutive integers is 96, what are the integers?

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