How close is close enough

A tap drips once every second. How much water is that in a day?

A millilitre (mL) is a small amount of water. 1000 mL make 1 litre.

The idea

The tap wastes about 4 litres in a day.

Exact values are not always needed. A rough estimate can show that an answer is reasonable or impossible.

Use three steps. First, imagine the situation. Next, choose the quantities that matter. Then estimate, and ask if the answer makes sense.

Here is the tap.

• One drip a second. A day has 60 × 60 × 24 = 86,400 seconds.
• So there are about 86,400 drips in a day.
• About 20 drips make 1 mL. One drip is about 0.05 mL.
• 86,400 × 0.05 = 4,320 mL. And 4,320 ÷ 1000 = 4.32 litres, about 4 litres.

Now compare with something you know. A bucket holds about 10 litres. Our 4 litres is less than one bucket. So it is believable. An answer of 400 litres would fill 40 buckets. That is not believable for a slow drip.

This check looks at the size of the answer. It does not prove the size of one drip.

Some jobs need exact values. Others need only a sense check. A sense check asks if the answer is sensible. Take 40 pupils who drink 2 glasses of 250 mL each. Each pupil drinks 2 × 250 = 500 mL. The class drinks 40 × 500 = 20,000 mL. That is 20 litres. An answer of 2 litres is far too small.