Home
Assignments
Bookmarks
Powers of ten
How do you write this in scientific notation? 0,12
The distance between the Earth and the Sun is about 150 billion metres. To avoid dealing with so many zeros, there's a little trick, that uses repeated multiplication by the number ten. This is what it looks like. Does it look complicated? Let's back up a bit and see how it works.
You know that exponential expressions are a way of writing repeated multiplications. X raised to the power of A means: X multiplied by itself A times. Exponential expressions with base 10 are especially useful, when dealing with very big or very small numbers. Multiplying by ten is easy. Just move the decimal point one step to the right, or add a zero at the end.
Every time you multiply by ten, move the decimal point one more step to the right. For powers of ten - exponential expressions with base ten - this means that the result is a one, followed by as many zeros as the power shows. 10 raised to the power of 9 is a "one" followed nine zeros - one billion. Instead of writing a long row of zeros, use a power of ten: write the number of zeros as the power. You can then multiply the power of ten expression by a more manageable number, for instance when you want to express the distance to the Sun.
That is 150 billion metres or 150 times ten to the power of 9 or One-point-five times ten to the power of 11 You can use the same method to write very small numbers as well. Negative powers of ten do the same thing, but instead you move the decimal point to the left so that you get a number smaller than one. The nucleus of a gold atom is approximately eight and a half millionths of a billionth of a metre in diameter, or eight and a half femtometres. To avoid a long row of zeros after the decimal point, we can write one femtometre as 10 - raised to the power of 'minus 15' - metres. The diameter of a gold atom nucleus is therefore 8 point 5, times ten to the power of minus-15 metres.
A power of ten is an exponential expression with base ten. When the exponent is positive, you move the decimal point as many places to the right as the power says. When the exponent is negative, you move the decimal point as many places to the left as the power says.