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Converting Percentages to Decimals Numbers

We are using percent (hundredths) and per mille (thousandths) due to the fact that our numeral system is made up of ones, tens, tenths and hundredths. Dividing by one hundred is the same as moving the decimal mark two places to the left. You have already used this rule in many examples so far.


Converting Between Percent and Decimal Numbers

  • When converting from percent to a decimal number, you remove the percent sign % and move the decimal mark two places to the left.

  • When converting a decimal number to percent, you add a percent sign % and move the decimal mark two places to the right.

The last rule is valid because an equality can be read both from left to right and from right to left.

What you need to remember about per mille is that it means thousandth, which means you have to move the decimal mark three places. Otherwise it is the exact same as when you work with percentages. Per mille is used way less than percentages, so the most important part is to know percentages. That’s also why I mostly focus on percentages here.

Example 1

Here I convert 6 % to a decimal number and back: 6% = 6 × 1 100 = 6 100 = 0.06 0.06 = 6 100 = 6 × 1 100 = 6%

Here I convert 75 % to a decimal number and back: 75% = 6 × 75 100 = 75 100 = 0.75 0.75 = 75 100 = 75 × 1 100 = 75%

You can see that the calculations on the top are just the opposite operations of the calculations on the bottom, and writing things twice is unnecessary.

Example 2

200% = 200 × 1 100 = 200 100 = 2.

200 % of a pizza is two pizzas. That’s twice as much as one pizza, or double the amount of pizza.

Moving the decimal mark two places is the same thing you do when you switch between meters and centimeters. You move two places to the left when you convert from centimeters to meters, and two places to the right when you convert from meters to centimeters.

Example 3

You get a similar computation when you convert 6 cm into meters by using decimal numbers. You use that 1cm = 1 100m, just like 1% = 1 100:

6cm = 6 × ( 1 100m) = (6 × 1 100) m = 6 100m = 0.06m.

Remember to move the decimal mark in the correct direction. If you’re not sure, use the trick that 1 = 100 100 and use the resulting fraction. You can also use these memory aids:


Moving the Decimal Mark in the Right Direction

Remember that cent in percent (per-cent) means hundredth, just like cent in centimeters means hundredth.

  • 6 % is a small part of the whole, just like 6 cm is a small part of 1 meter.

  • 60 % is between half and the entirety of a whole, just like 60 cm is between half a meter and a full meter.

  • 600% = 6 is 6 times as much as 1, just like 600cm = 6m is 6 times as long as one meter.

This rule can also be used when you’re looking at, for example, 7 % and 70 % or 9 % and 90 %. You can see that there is a big difference between 6 %, 60 % and 600 %. It’s very important to place the decimal mark correctly! There is a huge difference between $600 and $6, so make sure you don’t get fooled!

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Converting Percentages to Fractions