Question

1. how many significant figures are in the following numbers? (a) $78.9 pm 0.2$ (b) $3.788 \times 10^{9}$ (c) $2.46 \times 10^{-6}$ (d) $0.005 3$

Explanation:

Step1: Analyze 78.9 ± 0.2

In measured values with uncertainty, we use the certain value's significant figures. 78.9 has 3 non-zero digits, all significant.

Step2: Analyze $3.788 \times 10^9$

In scientific notation, all digits in the coefficient are significant. The coefficient 3.788 has 4 digits.

Step3: Analyze $2.46 \times 10^{-6}$

In scientific notation, all digits in the coefficient are significant. The coefficient 2.46 has 3 digits.

Step4: Analyze 0.0053

Leading zeros are not significant; only non-zero digits and trailing zeros after a decimal (if present) count. Here, 5 and 3 are significant, so 2 total.

Answer:

(a) 3
(b) 4
(c) 3
(d) 2