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 40 cm, and its length is 12 cm. What is its width?

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What is the value of x if log(x) + log(4) = log(32)?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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What is the area of an equilateral triangle with side length 10 cm?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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If the radius of a circle is 7 cm, what is its circumference?

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If x = 2 and y = 3, what is the value of (x^2 + y^2)?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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

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What is the length of the diagonal of a square with a side length of 7 cm?

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