Mathematics
Grade 7
15 min
Scientific notation
Scientific notation
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Introduction & Learning Objectives
Learning Objectives
Define scientific notation and explain its purpose.
Identify numbers correctly written in scientific notation.
Convert very large numbers from standard form to scientific notation.
Convert very small numbers from standard form to scientific notation.
Convert numbers written in scientific notation back to standard form.
Compare the magnitudes of numbers expressed in scientific notation.
Have you ever wondered how scientists talk about the distance to a star or the size of a tiny atom without writing endless zeros? 🌌🔬
In this lesson, you'll learn about scientific notation, a powerful way to write extremely large or extremely small numbers concisely. This skill is essential for understanding measurements in science, engineering, and everyday life, ma...
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Key Concepts & Vocabulary
TermDefinitionExample
Scientific NotationA compact way to write very large or very small numbers using powers of 10. It's written as a product of two factors: a coefficient (a number between 1 and 10) and a power of 10.The number 602,000,000,000,000,000,000,000 can be written as 6.02 × 10²³ in scientific notation.
Standard FormThe usual way of writing numbers, with all digits shown and no powers of 10.The number 93,000,000 is in standard form.
Coefficient (or Mantissa)The first part of a number in scientific notation. It must be a number greater than or equal to 1 and less than 10.In 3.45 × 10⁶, the coefficient is 3.45.
Base (10)The number that is raised to a power in scientific notation. It is always 10.In 3.45 × 10⁶, the base is 10.
ExponentThe power to which the base 10 is raised....
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Core Formulas
Converting Large Numbers to Scientific Notation
$$N = a \times 10^n$$ where $1 \le a < 10$ and $n$ is a positive integer.
To convert a large number (greater than or equal to 10) to scientific notation, move the decimal point to the left until there is only one non-zero digit to its left. The number of places you moved it becomes the positive exponent ($n$) of 10.
Converting Small Numbers to Scientific Notation
$$N = a \times 10^{-n}$$ where $1 \le a < 10$ and $-n$ is a negative integer.
To convert a small number (between 0 and 1) to scientific notation, move the decimal point to the right until there is only one non-zero digit to its left. The number of places you moved it becomes the negative exponent ($-n$) of 10.
Converting Scientific Notation to Standard Form...
5 more steps in this tutorial
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Challenging
The mass of a dust particle is 7.53 × 10⁻¹⁰ kg. The mass of a certain virus is 1.5 × 10⁻¹⁵ kg. Which is heavier and why?
A.The virus is heavier because its coefficient (1.5) is smaller.
B.The dust particle is heavier because its exponent (-10) is less negative than the virus's exponent (-15).
C.The virus is heavier because its exponent (-15) has a larger absolute value.
D.They have the same mass because the coefficients are different.
Challenging
A number in standard form is 305,000,000. It is written in scientific notation as $a \times 10^n$. What is the value of $a+n$?
A.11.05
B.313
C.3.13
D.11.5
Challenging
A student converts 0.00071. They correctly move the decimal 4 places to get a coefficient of 7.1. However, they write the final answer as 7.1 × 10⁴. Which statement best describes their error(s)?
A.They only made one error: the coefficient is wrong.
B.They only made one error: the sign of the exponent is wrong.
C.They made two errors: the coefficient is wrong AND the exponent is wrong.
D.They made no errors, the answer is correct.
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