Scientific Notation Study Guide
Introduction to Scientific Notation
I believe there are 15,747,724,136,275,002,577,605,653,961,181, 555,468,044,717,914,527,116,709,366,231,425, 076,185,631,031,296 protons in the universe and the same number of electrons.
—Sir Arthur Eddington (1882–1944)
How could you write the number 57,000,000,000 in a shorter, quicker way? This lesson will teach you about scientific notation and its advantages. Scientific notation is used to lessen the chance of leaving out a zero or misplacing a decimal point.
In the past, scientists found themselves with a problem when they had to work with really big numbers like 57,000,000,000 or really little numbers like 0.000000057. You see, scientists measure very large numbers, such as the distance from Earth to the sun, or very small numbers, such as the diameter of an electron.
To combat dealing with so many zeros, they came up with the idea to use shorthand to represent such extreme numbers. The shorthand, known as scientific notation, uses the powers of ten.
With scientific notation, instead of writing 57,000,000,000, you could write 5.7 × 1010. Instead of writing 0.000000057, you could write 5.7 × 10–8. The exponent of 10 tells whether the number is really big (a positive exponent) or really small (negative exponent).
The absolute value of the exponent tells how far the decimal point was moved to fit the pattern. Look at 7–9. The absolute value of –9 is 9, so you know the decimal point moved nine places:
To master scientific notation, you do not have to memorize the notation table. The trick to expressing a large number as a power of 10 is to move the decimal place over as many spaces as it takes for there to be one unit to the left of it. Then, add "× 10" and raise the 10 to the power that represents the number of times you moved the decimal point. Look at a huge number like 830,000,000,000,000 and count the places you'll need to move the decimal point.
You counted over 14 places, so 830,000,000,000,000 = 8.3 × 1014.
Let's try another example. Express 795,000,000 in scientific notation.
You counted over eight places, so 795,000,000 = 7.95 × 108.
Let's try this in reverse. Express 3.483 × 105 in standard form. You need to move the decimal point over the same as the power indicates. In this case, it would move five places.
3.483 . . . ?
Wondering how to do this when there are only three numbers shown to the right of the decimal place? Don't forget, you can use zeros as placeholders next to that 3. Actually, there are an unlimited number of zeros after that 3. But, you need to move only two more spaces:
3.483 × 105 in standard form is 348,300.
Find practice problems and solutions for these concepts at Scientific Notation Practice Questions.