Chapter 1: Our Number System 9
CHECK POINT
- Write 10,000 as a power of ten.
- Write 100,000,000,000 as a power of ten.
- Write 10^7 in standard notation.
- Wr ite 10^12 in standard notation.
- Write 10^5 in standard notation.
Scientific Notation
Suppose you needed to talk about the distance from Earth to Mars (which keeps changing because
both planets are moving, but you can give an approximate distance). You can say that Earth and
Mars are at least 34,796,800 miles apart and probably not more than 249,169,848 miles apart, so on
average, about 86,991,966.9 miles. If you read that last sentence and quickly lost track of what the
numbers were and replaced their names with a mental “oh, big number,” you’re not alone.
Whether they’re written as a string of digits like 34,796,800 or in words like two hundred
forty-nine million, one hundred sixty-nine thousand, eight hundred forty-eight, our brains have
trouble really making sense of numbers that large. (Whether you think the numbers or the words
are easier to understand is a personal matter. Our brains are not all the same.) Scientists and
others who work with very large or very small numbers on a regular basis have a method for
writing such numbers, called scientific notation.
Scientific notation is a system of expressing numbers as a number between one and ten, times a
power of ten. The first number is always at least 1 and less than 10. Ten and any number bigger
than ten can be written as a smaller number times a power of ten.
Let’s look at that with a few smallish numbers first. A single digit number like 8 would be 8 v
100. Ten to the zero power is 1, so 8 v 100 is 8 v 1 or 8. The number 20 would be 2 v 101. 10^1 is
10, so 2 v 101 is 2 v 10, or 20. For a larger number like 6,000,000 you would think of it as 6 v
1,000,000, or 6 v 106.
DEFINITION
Scientific notation is a method for expressing very large or very small numbers as the
product of a number between 1 and 10 and a power of 10.
