Question

1. round off each of these measurements to three significant figures.

a. 98.473 l
b. 0.000 763 21 cg
c. 57.048 m
d. 12.17°c
e. 0.007 498 3×10⁴ mm
f. 1764.9 ml

Explanation:

Step1: Identify significant - figure rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros are not significant. Trailing zeros are significant if there is a decimal point.

Step2: Round 98.473 L

The fourth digit 7 is greater than 5, so we round up the third digit. $98.473\approx98.5$ L.

Step3: Round 0.00076321 cg

The leading zeros are not significant. The fourth significant figure 2 is less than 5, so we keep the first three significant figures. $0.00076321\approx0.000763$ cg.

Step4: Round 57.048 m

The fourth significant figure 4 is less than 5, so we keep the first three significant figures. $57.048\approx57.0$ m.

Step5: Round 12.17°C

The fourth significant figure 7 is greater than 5, so we round up the third digit. $12.17\approx12.2$ °C.

Step6: Round $0.0074983\times10^{4}$ mm

First, rewrite it as $74.983$ mm. The fourth significant figure 8 is greater than 5, so we round up the third digit. $74.983\approx75.0$ mm or $0.00750\times 10^{4}$ mm.

Step7: Round 1764.9 mL

The fourth significant figure 4 is less than 5, so we keep the first three significant figures. $1764.9\approx1760$ mL.

Answer:

a. 98.5 L
b. 0.000763 cg
c. 57.0 m
d. 12.2 °C
e. $0.00750\times 10^{4}$ mm
f. 1760 mL