Estimate By Rounding to One Significant Figure Using Decimal Numbers

Let's say we wanted to guess how much a grain of sand weighs.

We might guess 0.01 grams or 0.005 grams.

We wouldn't usually guess 0.00429 grams..

This is because we are only interested in a rough idea of the amount, not an exact value.

When estimating we often use significant figures.

Have a look at this number: 0.0004851

There are 4 significant figures.

The 4 is the first significant figure, the 8 is the 2nd and so on, the 5 is the 3rd and the 1 is the 4th significant figure. 

Although we need them as placeholders, the zeros in this number are not significant. 

We start counting from the 1st non-zero digit. 

Let's look at another: 0.00989073

It has 6 significant figures.

We must still count the zero in between the 9 and 7 as significant this time. If we didn't count it, the place value of the other digits would change. 

When we're estimating numbers, a general rule to follow is to always round to 1 significant figure.

Example:

Estimate the following calculation:

0.045 + 0.81

We round each number to 1 significant figure i.e. after the 1st non-zero digit:

0.045 = 0.05

0.81 = 0.8

0.05 + 0.8 = 0.85

0.045 + 0.81 is approximately 0.85

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