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

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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What is the cube root of 729?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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If 8x = 512, what is the value of x?

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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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