Here’s a handy hack to help you handle all the zeros in standard form conversions.

Let’s look at the positive and negative power patterns that you may come across in your exams.

First up, the positive. For 10 to the power of 6, this is 10 multiplied by itself six times.

So, 10 times 10 times 10 times 10 times 10 times 10. There are six zeros after the 1 which, is 1 million.

10 to the power of 5 is five zeros after the 1, which is 100,000.

10 to the power of 4 has four zeros after the 1, which equals 10,000. 10 to the power of 3 has three zeros, which is 1000.

10 to the power of 2 has two zeros, which is 100.

10 to the power of 1 has one zero, which is 10, and 10 to the power of 0 is no zeros, so just one.

But, when working with standard form numbers that have a negative power of 10, it’s not quite as simple.

10 to the power of negative 6 is 1 divided by 10 multiplied by itself six times. So, 10 times. 10 times. 10 times. 10 times. 10 times 10, which is one divided by a million, which equals 0.000001.

Notice how there are only five zeros after the decimal point. This is one less than the value of the power.

And this is the same for all negative powers of 10.

10 to the power of negative 6 has five zeros after the decimal point, which equals 0.000001.

10 to the power of negative 5 has four zeros after the decimal point, which is 0.00001.

10 to the power of negative 4 has three zeros after the decimal point.

10 to the power of negative 3 has two zeros.

10 to the power of negative 2 has one zero, so it’s 0.01.

10 to the power of negative 1 has no zeros after the decimal point, so it’s just 0.1.

Putting in an extra zero for negative power conversions is a common mistake, so try and remember that negative powers mean one fewer zero than the power after the decimal point.