Question

1. for each number, underline the zeros that are significant and draw a line through the zeros that are not:

a. 1 050 501 km
b. 0.0020 m
c. 0.000000000000002 s
d. 0.001090 cm

1. for each number, underline the zeros that are significant and draw a line through the zeros that are not:

a. 180 701 mi
b. 0.001040 m
c. 0.005710 km
d. 90 201 m

1. how many significant figures are in each number?

a. 0.000312 m
b. 312 000 s
c. 3.12×10^5 km
d. 13 127 s
e. 2000

Explanation:

51

• a. 1 050 501 km:
• The zeros between non - zero digits are significant. So, 1 $\underline{0}$5$\underline{0}$ 5$\underline{0}$1 km.
• b. 0.0020 m:
• Leading zeros are not significant. Trailing zero after a non - zero digit in a decimal is significant. So, 0.002$\underline{0}$ m.
• c. 0.0000000000000002 s:
• All leading zeros are not significant. So, 0.0000000000000002 s (no significant zeros).
• d. 0.001090 cm:
• Leading zeros are not significant. Zeros between non - zero digits and trailing zero after non - zero digit in a decimal are significant. So, 0.001$\underline{0}$9$\underline{0}$ cm.

52

• a. 180 701 mi:
• Zeros between non - zero digits are significant. So, 18$\underline{0}$ 7$\underline{0}$1 mi.
• b. 0.001040 m:
• Leading zeros are not significant. Zeros between non - zero digits and trailing zero after non - zero digit in a decimal are significant. So, 0.001$\underline{0}$4$\underline{0}$ m.
• c. 0.005710 km:
• Leading zeros are not significant. Trailing zero after non - zero digits in a decimal is significant. So, 0.00571$\underline{0}$ km.
• d. 90 201 m:
• Zeros between non - zero digits are significant. So, 9$\underline{0}$ 2$\underline{0}$1 m.

53

• a. 0.000312 m:

Step1: Identify significant figures rule

Non - zero digits are always significant. Leading zeros are not significant.

Step2: Count significant figures

The significant figures are 3, 1, 2.

Step1: Identify significant figures rule

Trailing zeros in a whole number without a decimal point may or may not be significant. Assuming no other context, we consider non - zero digits significant.

Step2: Count significant figures

The significant figures are 3, 1, 2.

Step1: Identify significant figures rule

In scientific notation, the digits in the coefficient are significant.

Step2: Count significant figures

The significant figures are 3, 1, 2.

Answer:

3

• b. 312 000 s: