topic 1: significant figures
1. determine the number of significant figures in each of the following:
a. 0.7540
b. 12500
c. 1.01
d. 1200
e. 1.04 * 103
f. 0.0080050

These are 6 questions and 6 answers, each with its explanation.

Explanation:

a. 0.7540

When there are not digits (non-zero digits) before the decimal point, the significant digits are all the decimal digits from the first non-zero decimal. So, in this case, they are all the shown digits: 7, 5, 4, and 0, i.e. 4 significant figures.

b) 12500

When there is not decimal point, the significant digits include all the digits before only zeros appear. So, they are 1, 2, and 5, i.e. 3 significant figures.

When it is meant that all the digits are significan, a perod must be added, in this way: 12500. The last point is part of the number, it does not add value, but indicates that all the digits are significant.

c) 10000.01

This is the only number from the list with both decimal and non-decimal digits.

When there are digits before and after the decimal point, the significant digits include all the digits before the decimal point and all the decimal digits. So they are 1, 0, 0, 0, 0, 0, and 1, i.e. 7 significant digits.

d) 1200

Again, when there is not decimal point, the significant digits include all the digits before only zeros appear. So, they are 1 and 2, i.e. 2 significant figures.

The two last zeros do not count as significant digits. If the number were written 1200., i.e. showing a decimal point but without digits after the decimal point, then all the four digits were singnificant.

e) 1.04 × 10⁴

This number is written in scientific notation.

The numbers before the power of 10 are called mantissa.

For a number written in scientific notation, the significant digits are the digits in the mantissa, i.e. 1.04. So, the number of significant digits is 3 (1, 0, and 4).

f) 0.0080050

For a number with only decimal digits (there are not digits with value before the decimal point), the zeros after the decimal point and before the first non-zero digit do not count as significant figures. So, the significant figures are: 8, 0, 0, 5, and 0, i.e. 5 significant figures.

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