Estimating (Multiplication)

When we don’t need a precise answer, it is helpful to confidently estimate within a good error margin. For example, if buying lumber, you need to buy 42 feet at 5.83 per foot, what is the ball park for the price?

One method is to round each value to one significant figure:

42 simplifies to 40

5.83 simplifies to 6

Now lets take 40 \times 6 = 4 \times 10 \times 6 = 4 \times 6 \times 10 = 24 \times 10 = 240.

Now, using a calculator we find that

42 \times 42 = 244.86.

We underestimated, but not by very much. As a percentage of the precise answer, our estimate is out by 1.98%.

In this context of practising arithmetic, a good estimate is within 10% of the precise answer. An excellent estimate is within 5% of the precise answer.

Another example: 422 \times 5123.

Now, 422 simplifies to 400, or 4 \times 100.

5123 simplifies to 5000, or 5 \times 1000.

So we have 422\times5123 \approx 4\times 5 \times 100 \times 1000 = 20 \times 100\,000= 2\,000\,000

Using a calculator, we find that 422 \times 5123 = 2161906.

Our error is 7.49%.

Try it out!

Up to 100 multiplied by 100

A little more difficult

Done here – go back to the Numeracy Menu