Question

1. underline all of the significant digits in the following values.

a. 94,000 m
b. 7200 apples
c. 0.004380 g
d. 400.0 kg
e. 80,050 s
f. 1000 g = 1 kg

Explanation:

Step1: Rules for significant digits

Non - zero digits are always significant. Zeros between non - zero digits are significant. Trailing zeros in a number with a decimal point are significant. Leading zeros are not significant. Trailing zeros in a whole number without a decimal point may or may not be significant (usually considered not significant for measurement values).

Step2: Analyze 94,000 m

Non - zero digits 9 and 4 are significant. Trailing zeros without a decimal point are not significant. So, $\underline{9}\underline{4}$,000 m

Step3: Analyze 7200 apples

Non - zero digits 7 and 2 are significant. Trailing zeros without a decimal point are not significant. So, $\underline{7}\underline{2}$00 apples

Step4: Analyze 0.004380 g

Leading zeros are not significant. Non - zero digits 4, 3, 8 and the trailing zero are significant. So, 0.00$\underline{4}\underline{3}\underline{8}\underline{0}$ g

Step5: Analyze 400.0 kg

Non - zero digit 4 is significant. Zeros between non - zero digit and decimal point and trailing zero after decimal point are significant. So, $\underline{4}\underline{0}\underline{0}\underline{.}\underline{0}$ kg

Step6: Analyze 80,050 s

Non - zero digits 8 and 5 are significant. Zero between 8 and 5 is significant. Trailing zero without decimal point is not significant. So, $\underline{8}\underline{0}$,$\underline{0}\underline{5}$0 s

Step7: Analyze 1000 g = 1 kg

In the conversion factor 1000 g = 1 kg, the 1 in 1 kg and the 1000 (as a defined conversion) are exact numbers and have infinite significant digits. But if we consider 1000 g as a measured value, non - zero digit 1 is significant and trailing zeros without decimal point are not significant. So, $\underline{1}$000 g = 1 kg

Answer:

a. $\underline{9}\underline{4}$,000 m
b. $\underline{7}\underline{2}$00 apples
c. 0.00$\underline{4}\underline{3}\underline{8}\underline{0}$ g
d. $\underline{4}\underline{0}\underline{0}\underline{.}\underline{0}$ kg
e. $\underline{8}\underline{0}$,$\underline{0}\underline{5}$0 s
f. $\underline{1}$000 g = 1 kg