# 02 Decimal Percentages

Earlier, we decided that equations were a pretty efficient way to find percentages.

It was easy enough to use a double number line diagram to find the value that corresponded to certain percent increases or decreases. So far, the percentages have been easy enough to show on the number line, like 20, 40, 25, etc. But what if the percentage was a decimal, like 7.8% or 3.75? These would be a little difficult to show on the number line.

But such percentage problems are pretty much solved the same way as any other percentages.

Say your height was 160 cm last year. This year, you noticed that your height increased by 3.75 percent. How much is your new height?

An increase in 3.75 % can be found by adding the initial height to the increased height of 3.75%. Initial height + Increased height = 160 + 3.75% of 160 100% of 160 + 3.75% of 600 (100 + 3.75)% x 160 = 103.75% x 160 = 166 cm

The increased amount seems to be 6 cm, which is given by 3.75% of 160. Easy right?

You can also use decimals instead:

3.75% is 0.0375. So, our increased height is 0.0375 x 160. Adding this to the original, we have 160 + 0.0375 x 160 = (1 + 0.0375) x 160 = 166 cm!

Remember that the same applies to percent decrease as well.

You scored 78 marks in your first term. Sadly, in the second term, your marks decreased by about 7.4 percent! How much did you score?

Your second term score = First term score - 7.4% of First term score = 100% of 78 - 7.4% of 78 = (100 - 7.4)% x 78 = 92.2% x 78 = 71.916 marks!

92.2% of first term marks is your new second term marks!

Alternatively, using decimals, we have Your second term score = First term score - 7.4% of First term score = 78 - 0.074 x 78 = (1-0.074) x 78 = 0.922 x 78 = 71.916 marks

While solving such problems with decimal percentages, do be mindful of the numbers after the decimal point. Sometimes you might get confused with 3.5% being 0.35 instead of 0.035.