A student asks… about percentages

A student asks:

Why do you multiply by 1.07 if you're adding 7%? I thought 7% was 0.07.

You're quite right - 0.07 is exactly the same thing as 7% (and, if you like, $\frac{7}{100}$). However, if you're adding on 7%, you need to multiply by 1.07, and here's why.

Let's say you're adding 7% to 1000: you'd be working out $1000 + 1000 \times 0.07$ - or, better still, $1000\left( 1 + 0.07 \right)$. That thing in the bracket is 1.07.

The short reason: because you're adding 7% on to what's already there, you need to multiply it by 1 + the percentage as a decimal.

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

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I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

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