Antimatter: does it matter?

Scientific notation: what does 10¹⁵ mean?

Everyday numbers

Most of the time we write numbers as a series of digits: 1234, for example.

This works pretty well for most of the numbers we need in our daily lives. It’s easy to see that 1500 is bigger than 150, or that 0.05 is smaller than 0.5.

Extreme numbers

But when numbers get very big or very small, our normal method of writing numbers can make them hard to read.

• Which is bigger: 100000000000 or 50000000000 ?
• Which is smaller: 0.000000000006 or 0.00000000003 ?

Our normal method of writing numbers doesn’t work so well for these numbers. To make very large and very small numbers clearer, we use “scientific notation”.

Large numbers

• Instead of writing 1000000000000000 (a 1 followed by fifteen zeroes), we can write 10¹⁵, and say “ten to the power fifteen”.
• The number 2000000000000000 (a 2 followed by fifteen zeroes) is two times 10¹⁵, so we write 2 x 10¹⁵ and say “two times ten to the power fifteen”.

It can be hard to tell the difference between 1000000000000000 and 100000000000000, but it’s easy to see that 10¹⁵ (“ten to the power fifteen”) is bigger than 10¹⁴ (“ten to the power fourteen”).

Small numbers

Small numbers work the same way.

• Instead of writing 0.000000000000001 (a decimal point with fifteen zeroes, followed by a 1), we can write 10^-15 and say “ten to the power minus fifteen”.
• The number 0.000000000000003 is three times 10^-15, so we write 3 x 10^-15 and say “three times ten to the power minus fifteen”.

It isn’t always easy to tell the difference between 0.000000000000001 and 0.00000000000001, but we can see at a glance that 10^-15 (“ten to the power minus fifteen”) is smaller than 10^-14 (“ten to the power minus fourteen”).

How to read a number in scientific notation

When we say “ten to the power…” it’s the power that really tells us how big or small our number is.

• The power tells us how many zeroes are in the number, so the bigger the power, the more extreme the number is.
• If the power has a minus sign, it’s a number smaller than 1; if there’s no minus sign in the power, it’s a number larger than 1.

Some examples

• 10¹² is a 1 followed by twelve zeroes, so it’s 1 000 000 000 000.
• 10^-8 has a minus sign in its power, so it’s a 1 PRECEDED by eight zeroes (counting the zero before the decimal point). That’s 0.00000001.