Question

1. how many significant figures are in the following measurements?

a. 300 000 000 m/s
b. 3.00 × 10⁸ m/s
c. 25.030°c
d. 0.006 070°c
e. 1.004 j
f. 1.305 20 mhz

Explanation:

Part a: \( 300000000 \, \text{m/s} \)

Step 1: Recall significant figure rules for trailing zeros without a decimal.

Trailing zeros in a whole number without a decimal are ambiguous. Here, the non - zero digit is 3, and the trailing zeros may be placeholders. So, only the non - zero digit 3 is significant.

Step 1: Recall significant figures in scientific notation.

In scientific notation \( a\times10^{n} \), the significant figures are in the coefficient \( a \). For \( 3.00\times 10^{8} \), the coefficient is 3.00. All the digits in the coefficient (3, 0, 0) are significant.

Step 1: Recall significant figure rules for decimals and trailing zeros.

• All non - zero digits are significant: 2 and 5 are significant.
• Zeros between non - zero digits are significant: the 0 between 5 and 3 is significant.
• Trailing zeros after a decimal are significant: the last 0 is significant.
• The digits are 2, 5, 0, 3, 0. Count them: 2,5,0,3,0. So there are 5 significant figures.

Answer:

1

Part b: \( 3.00\times10^{8} \, \text{m/s} \)