Question

1. how many significant figures does each of the following measurements have? (if it will help you make notes by these to show how to figure them out.)

a) 100 s
b) 100. m/s
c) 101.00 m
d) 0.0011 ng
e) 0.0001 ps
f) 10.0 ml
g) 1.0 x 10¹³ degrees c
h) 110,000 cm
i) 1.111 x 10⁻⁸ j

1. round each of the following measurements to the number of significant figures specified. write your answers in scientific notation.

a) 10,000 s (3 sigfigs)
b) 0.03970 ng (2 sigfigs)
c) 75.54 g (2 sigfigs)
d) 0.1 m (2 sigfigs)

1. calculate each of the following and keep the proper # of sig figs or proper place value.

a) 12 m + 12.1 m
b) 12 m x 12.0 m
c) 0.01 g − 0.001 g
d) 120.00 m / 10.0 hr

Explanation:

Question 9

Step1: Apply sig fig rules to each value

• Trailing zeros without decimal are ambiguous, count non-zeros; trailing zeros after decimal are significant; leading zeros are not; all digits in scientific notation (coefficient) are significant.

Step2: Count significant figures for each

a) $100\ \text{s}$: Trailing zeros no decimal → 1 sig fig
b) $100.\ \text{m/s}$: Decimal present, all digits count → 3 sig figs
c) $101.00\ \text{m}$: Zeros after decimal and between non-zeros count → 5 sig figs
d) $0.0011\ \text{ng}$: Leading zeros ignored, non-zeros count → 2 sig figs
e) $0.0001\ \text{ps}$: Leading zeros ignored, 1 non-zero → 1 sig fig
f) $10.0\ \text{mL}$: Zeros after decimal and between count → 3 sig figs
g) $1.0 \times 10^{13}\ \text{degrees C}$: Coefficient digits count → 2 sig figs
h) $110,000\ \text{cm}$: Trailing zeros no decimal → 2 sig figs
i) $1.111 \times 10^{-8}\ \text{J}$: Coefficient digits count → 4 sig figs

Step1: Round to specified sig figs

Adjust each value to the required number of significant figures, then convert to scientific notation ($a \times 10^n$, $1 \leq a < 10$).

Step2: Convert to scientific notation

a) $10,000\ \text{s}$ (3 sig figs): Round to $1.00 \times 10^4$
b) $0.03970\ \text{ng}$ (2 sig figs): Round to $4.0 \times 10^{-2}$
c) $75.54\ \text{g}$ (2 sig figs): Round to $7.6 \times 10^1$
d) $0.1\ \text{m}$ (2 sig figs): Convert to $1.0 \times 10^{-1}$

Step1: Perform arithmetic operation

a) $12\ \text{m} + 12.1\ \text{m} = 24.1\ \text{m}$; round to least decimal place (12 has 0 decimals)
b) $12\ \text{m} \times 12.0\ \text{m} = 144\ \text{m}^2$; round to least sig figs (12 has 2)
c) $0.01\ \text{g} - 0.001\ \text{g} = 0.009\ \text{g}$; round to least decimal place (0.01 has 2 decimals)
d) $\frac{120.00\ \text{m}}{10.0\ \text{hr}} = 12.000\ \text{m/hr}$; round to least sig figs (10.0 has 3)

Step2: Round to proper sig figs/place

a) Round $24.1$ to 0 decimals → 24
b) Round $144$ to 2 sig figs → 140
c) $0.009$ matches required decimal place
d) Round $12.000$ to 3 sig figs → 12.0

Answer:

a) 1
b) 3
c) 5
d) 2
e) 1
f) 3
g) 2
h) 2
i) 4

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Question 10