State the number of significant figures in the following numbers: a) 0.006 m², b) 2.65 × 10 kg, c) 0.2309…

Question

State the number of significant figures in the following numbers: a) 0.006 m², b) 2.65 × 10 kg, c) 0.2309 in³, d) 1000 seconds, e) 10.006032 m², f) 1001000A

ScanSolve AI Tutor · Accepted Answer

Here are the number of significant figures for each value:

a) $0.006 \text{ m}^2$

Leading zeros (zeros before non-zero digits) are not significant.
The only significant digit is 6.
The number of significant figures is $\boxed{1}$ .
- b) $2.65 \times 10^4 \text{ kg}$
In scientific notation, all digits in the coefficient (2.65) are significant.
The number of significant figures is $\boxed{3}$.
- c) $0.2309 \text{ in}^3$
The leading zero is not significant.
The digits 2, 3, 0, and 9 are significant (the 0 is a "sandwich" zero between non-zero digits).
The number of significant figures is $\boxed{4}$ .
- d) $1000 \text{ seconds}$
When a number does not contain a decimal point, trailing zeros are generally considered not significant unless specified otherwise (e.g., by adding a decimal point).
Only the digit 1 is significant.
The number of significant figures is $\boxed{1}$ .
- e) $10.006032 \text{ m}^2$
All non-zero digits are significant.
Zeros between non-zero digits are significant. Zeros to the right of the decimal point and between non-zero digits are also significant.
The digits 1, 0, 0, 0, 6, 0, 3, 2 are all significant.
The number of significant figures is $\boxed{8}$ .
- f) $1001000 \text{ A}$
The non-zero digits (1 and 1) are significant.
The zeros between non-zero digits (00) are significant. The trailing zeros (000) are not significant because there is no decimal point.
The number of significant figures is $\boxed{4}$ .

State the number of significant figures in the following numbers: a) 0.006 m², b) 2.65 x 10 kg, c) 0.2309 in³, d) 1000 seconds, e) 10.006032 m², f) 1001000A

Step-by-step solution

Leading zeros (zeros before non-zero digits) are not significant.

In scientific notation, all digits in the coefficient (2.65) are significant.

The leading zero is not significant.

When a number does not contain a decimal point, trailing zeros are generally considered not significant unless specified otherwise (e.g., by adding a decimal point).

All non-zero digits are significant.

The non-zero digits (1 and 1) are significant.

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