Question

Let us convert a measured length of 4.700 m into different units. Keeping in view the number of significant figures, which of the following is not a correct method of converting the units? *
(a) 4.700 m = 4.700 × 10² cm
(b) 4.700 m = 4.700 × 10³ mm
(c) 4.700 m = 4700 mm
(d) 4.700 m = 4.700 × 10³ km

Answer 1

Given : a measured length of 4.700 m into different units.

To Find :  Keeping in view the number of significant figures, which of the following is not a correct method of converting the units

(a) 4.700 m = 4.700 × 10² cm

(b) 4.700 m = 4.700 × 10³ mm

(c) 4.700 m = 4700 mm

(d) 4.700 m = 4.700 × 10⁻³ km

Solution:

All non-zero digits are significant.

The leftmost nonzero digit is the first or most significant figure.

If there is a decimal point, the rightmost digit is the last or least significant figure

If there is no decimal point explicitly shown, the rightmost non-zero digit is the least significant figure

All digits between the most significant figure and the least significant figure are significant.

4.700    4 Significant Figures

4.700 × 10²   4 Significant Figures

4.700 × 10³  4 Significant Figures

4700   has only 2  Significant Figures

4.700 × 10⁻³  4 Significant Figures

Hence 4.700 m = 4700 mm  is not correct method of converting the units

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Answer 2

$\sf(b) \: \longmapsto \: \: 4.7 \times {10}^{3} \: mm$