Chapter 1, Problem 19E

Interpretation Introduction

(a)

Interpretation:

The $\text{3984}\text{.6 }$ number should be expressed in four significant figures.

Concept introduction:

All nonzero digits are significant and zeros are significant, if preceding the decimal point, or following the decimal point and preceding the first nonzero digit, are not significant.The case of terminal zeros that precede the decimal point in quantitiesgreater than one is ambiguous.

Therule of rounding off is to increase the final digit by one unit if the digitdropped is 5, 6, 7, 8, or 9 and to leave the final digit unchanged if the digitdropped is 0, 1, 2, 3, or 4.

Interpretation Introduction

(b)

Interpretation:

The number $\text{422}\text{.04}$ should be expressed in four significant figures.

Concept introduction:

All nonzero digits are significant and zeros are significant, if preceding the decimal point, or following the decimal point and preceding the first nonzero digit, are not significant. The case of terminal zeros that precede the decimal point in quantitiesgreater than one is ambiguous.

Therule of rounding off is to increase the final digit by one unit if the digitdropped is 5, 6, 7, 8, or 9 and to leave the final digit unchanged if the digitdropped is 0, 1, 2, 3, or 4.

Interpretation Introduction

(c)

Interpretation:

The number 186,000 should be expressed in four significant figures.

Concept introduction:

All nonzero digits are significant and zeros are significant, if preceding the decimal point, or following the decimal point and preceding the first nonzero digit, are not significant. The case of terminal zeros that precede the decimal point in quantitiesgreater than one is ambiguous.

Therule of rounding off is to increase the final digit by one unit if the digitdropped is 5, 6, 7, 8, or 9 and to leave the final digit unchanged if the digitdropped is 0, 1, 2, 3, or 4.

Interpretation Introduction

(d)

Interpretation:

The number 33900 should be expressed in four significant figures.

Concept introduction:

All nonzero digits are significant and zeros are significant, if preceding the decimal point, or following the decimal point and preceding the first nonzero digit, are not significant. The case of terminal zeros that precede the decimal point in quantitiesgreater than one is ambiguous.

Therule of rounding off is to increase the final digit by one unit if the digitdropped is 5, 6, 7, 8, or 9 and to leave the final digit unchanged if the digitdropped is 0, 1, 2, 3, or 4.

Interpretation Introduction

(e)

Interpretation:

The number $6.321\times {10}^4$ should be expressed in to four significant figures.

Concept introduction:

All nonzero digits are significant and zeros are significant, if preceding the decimal point, or following the decimal point and preceding the first nonzero digit, are not significant. The case of terminal zeros that precede the decimal point in quantitiesgreater than one is ambiguous.

Therule of rounding off is to increase the final digit by one unit if the digitdropped is 5, 6, 7, 8, or 9 and to leave the final digit unchanged if the digitdropped is 0, 1, 2, 3, or 4.

Interpretation Introduction

(f)

Interpretation:

The number $\text{5}\text{.0472}\times {10}^{\text{-}4}$ should be expressed in to four significant figures.

Concept introduction:

All nonzero digits are significant and zeros are significant, if preceding the decimal point, or following the decimal point and preceding the first nonzero digit, are not significant. The case of terminal zeros that precede the decimal point in quantitiesgreater than one is ambiguous.

Therule of rounding off is to increase the final digit by one unit if the digitdropped is 5, 6, 7, 8, or 9 and to leave the final digit unchanged if the digitdropped is 0, 1, 2, 3, or 4.