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

What is the sum of the first 20 odd numbers?

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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What is the LCM of 15 and 20?

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

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What is the greatest common divisor (GCD) of 36 and 48?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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A man spends 75% of his income and saves Rs. 600. What is his total income?

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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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