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Approximation

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Significant figures - decimals

Rounding 12.756 or 4.543 to 1 decimal place (d.p.) seems sensible, as the rounded figures are very close to the actual value.

12.756 = 12.8 (1 d.p.)
4.543 = 4.5 (1 d.p.)

But what happens if you round a very small number to 1 d.p?

0.00546 = 0.0 (1 d.p.)
0.00213 = 0.0 (1 d.p.)

This is not a useful answer. Another way to find an approximate answer with very small numbers is to use significant figures.

Counting significant figures

Significant figures start at the first non-zero number, so ignore the zeros at the front, but not the ones in between. Look at the following examples:

0.0071
0.0345

From the first significant figure onwards, all zeros are included. It's only the zeros at the beginning that don't count.

Question

How many significant figures do the following numbers have?

a) 0.3007
b) 2.01
c) 0.001023

Answer

a) 0.3007 has four significant figures.
b) 2.01 has three significant figures.
c) 0.001023 has four significant figures.

Activity

Approximation activity

Round up, round up and try this activity!

Play

Elemental

Can you conquer the elements?

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