In this Grade 8 Saxon Math Course 3 lesson, students learn to write very large numbers using scientific notation, expressing them as a coefficient (a decimal with one non-zero digit to the left of the decimal point) multiplied by a power of 10. The lesson covers converting numbers like 93,000,000 into the form 9.3 × 10⁷ and interpreting how the exponent corresponds to decimal point placement. Students also practice reading and writing numbers in both scientific notation and standard form, including recognizing how calculators display results in scientific notation.
Section 1
📘 Scientific Notation for Large Numbers
Scientific notation is a method of writing a number as a decimal number times a power of 10.
Now that you have the big idea, you will master converting between standard form and scientific notation through guided examples and practice problems.
Section 2
Scientific Notation
Scientific notation is a method of writing a number as a decimal number times a power of 10. The coefficient is written with one non-zero digit to the left of the decimal point.
The speed of light, 300,000,000 meters per second, is written as .
One trillion, or 1,000,000,000,000, is written as .
'Two point five times ten to the sixth' is written as .
Imagine writing the distance to a star with all its zeros! Scientific notation is a superhero shortcut that tidies up gigantic numbers into a neat package with a coefficient and a power of 10. The exponent tells you how many places the decimal point moved, saving you from writing an endless trail of zeros.
Section 3
Standard to Scientific Notation
To write a number in scientific notation, place the decimal point after the first non-zero digit to create the coefficient. The exponent on the 10 is the number of places the decimal point moved.
To convert 93,000,000: Move the decimal 7 places left to get 9.3, so it's .
To convert 365,000: Move the decimal 5 places left to get 3.65, so it's .
To convert 25 million (25,000,000): Move the decimal 7 places left to get 2.5, so it's .
Think of it as a decimal point adventure! To convert a big number, slide the decimal to the left until only one hero digit remains in front. The number of slides you made is your superpower exponent. This makes huge numbers like the distance to the sun much easier to handle without getting lost in all those zeros.
Section 4
Scientific Notation to Standard Form
To write a scientific notation number in standard form, move the decimal point to the right. The exponent on the 10 tells you how many places to move it.
Time to unleash the zeros! The exponent tells you how many spots to shift the decimal point to the right, turning a compact expression back into its full, magnificent size. Just add zeros to fill in the empty spaces you create on the way. It’s like watching a tiny number grow into a giant before your very eyes!
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Section 1
📘 Scientific Notation for Large Numbers
Scientific notation is a method of writing a number as a decimal number times a power of 10.
Now that you have the big idea, you will master converting between standard form and scientific notation through guided examples and practice problems.
Section 2
Scientific Notation
Scientific notation is a method of writing a number as a decimal number times a power of 10. The coefficient is written with one non-zero digit to the left of the decimal point.
The speed of light, 300,000,000 meters per second, is written as .
One trillion, or 1,000,000,000,000, is written as .
'Two point five times ten to the sixth' is written as .
Imagine writing the distance to a star with all its zeros! Scientific notation is a superhero shortcut that tidies up gigantic numbers into a neat package with a coefficient and a power of 10. The exponent tells you how many places the decimal point moved, saving you from writing an endless trail of zeros.
Section 3
Standard to Scientific Notation
To write a number in scientific notation, place the decimal point after the first non-zero digit to create the coefficient. The exponent on the 10 is the number of places the decimal point moved.
To convert 93,000,000: Move the decimal 7 places left to get 9.3, so it's .
To convert 365,000: Move the decimal 5 places left to get 3.65, so it's .
To convert 25 million (25,000,000): Move the decimal 7 places left to get 2.5, so it's .
Think of it as a decimal point adventure! To convert a big number, slide the decimal to the left until only one hero digit remains in front. The number of slides you made is your superpower exponent. This makes huge numbers like the distance to the sun much easier to handle without getting lost in all those zeros.
Section 4
Scientific Notation to Standard Form
To write a scientific notation number in standard form, move the decimal point to the right. The exponent on the 10 tells you how many places to move it.
Time to unleash the zeros! The exponent tells you how many spots to shift the decimal point to the right, turning a compact expression back into its full, magnificent size. Just add zeros to fill in the empty spaces you create on the way. It’s like watching a tiny number grow into a giant before your very eyes!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter