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How many significant digits are in the number 1.30 x 10⁴?

User Denski
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Final answer:

The number 1.30 x 10⁴ has three significant figures, where the '1', '3', and trailing zero after the decimal point are all significant, the latter indicating precision to the tenths place.

Step-by-step explanation:

The number 1.30 x 10⁴ has three significant figures. When writing numbers in scientific notation, all the digits that are not placeholders are considered significant. Therefore, in the number 1.30 x 10⁴, the digit '1' is significant, as is the digit '3', and because there is a decimal followed by a zero, the zero is also significant. It indicates that the measurement was precise to the tenths place, so it counts as a significant figure.

In summary, zeros can be significant except when they serve only as placeholders. For instance, in the number 1300, written in standard form without a decimal, it is unclear if the zeros are placeholders or significant figures. However, by using scientific notation:

  • 1.3 × 10³ signifies two significant figures.
  • 1.30 × 10³ signifies three significant figures.
  • 1.400 × 10³ signifies four significant figures.

Therefore, the scientific notation 1.30 x 10⁴ unambiguously indicates that there are three significant figures in the number.

User Makwana Ketan
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