Question

Please help with significant figures

Answer 1

Certainly! Significant figures are digits in a number that contribute to its precision. When performing calculations or working with numbers, it's important to maintain the correct number of significant figures to ensure accuracy.

Here are the rules for determining significant figures:

1. Non-zero digits are always significant. For example, 1, 2, 3, ... 9 are all significant.

2. Leading zeros (zeros at the beginning of a number) are not significant. For example, in the number 0.005, the leading zero is not significant.

3. Captive zeros (zeros between non-zero digits) are always significant. For example, in the number 1004, both zeros are significant.

4. Trailing zeros (zeros at the end of a number) are significant only if they are after a decimal point. For example, in the number 1200, the two trailing zeros are not significant, but in 1200.0, they are.

5. Zeros used solely for spacing the decimal point (placeholders) are not significant. For example, in 0.0072, only the two non-zero digits are significant.

When performing calculations, the result should be rounded to match the least number of significant figures in the original values.

For example, if you have two values: 23.45 and 6.2, when you divide them, you would round your answer to the least number of significant figures in the original values, which is two significant figures in this case.

Remember that addition and subtraction should be rounded to the least number of decimal places in the original values.

If you have specific numbers or calculations you're working with, feel free to share them, and I can help you determine the correct significant figures for the result.

Answer 2

Significant figures are the digits in a number that are known to be accurate and reliable. They are used to indicate the precision of a measurement or calculation.

For the question:
Add:

1.
`\sf 16.5 \: \text{cm} + 8 \, \text{cm} + 4.37 \, \text{cm} = 28.87 \, \text{cm} \approx 28.9 \, \text{cm}`

2.
`\sf013.25 \, \text{g} + 10.00 \, \text{g} + 9.6 \, \text{g} = 32.85 \, \text{g} \approx 32.9 \, \text{g}`

3.
`2.36 \, \text{m} + 3.38 \, \text{m} + 0.355 \, \text{m} + 1.06 \, \text{m} = 7.155 \, \text{m} \approx 7.16 \, \text{m}`

4.
`0.0853 \, \text{g} + 0.0547 \, \text{g} + 0.037 \, \text{g} + 0.00387 \, \text{g} = 0.18087 \, \text{g} \approx 0.18\, \text{g}`

Subtract:

1.
`\sf 23.27 \, \text{km} - 12.058 \, \text{km} = 11.212 \, \text{km} \approx 11.2 \, \text{km}`

2.
`\sf 13.57 \, \text{g} - 6.3 \, \text{g} = 7.27 \, \text{g} \approx 7.3 \, \text{g}`

3.
`350.0 \, \text{m} - 200 \, \text{m} = 150.0 \, \text{m} \approx 150 \, \text{m}`

4.
`27.68 \, \text{cm} - 14.369 \, \text{cm} = 13.311 \, \text{cm} \approx 13.31 \, \text{cm}`

Multiply:

1.
`2.6 \, \text{cm} * 3.78 \, \text{cm} = 9.828 \, \text{cm}^2 \approx 9.83 \, \text{cm}^2`

2.
`6.54 \, \text{m} * 0.37 \, \text{m} = 2.4198 \, \text{m}^2 \approx 2.42 \, \text{m}^2`

3.
`0.036 \, \text{m} * 0.02 \, \text{m} = 0.00072 \, \text{m}^2 \approx 0.0007 \, \text{m}^2`

4.
`35.7 \, \text{cm} * 0.78 \, \text{cm} * 2.3 \, \text{cm} = 64.0458 \, \text{cm}^3 \approx 64.05 \, \text{cm}^3`

Divide:

1.
`\frac{35 \, \text{cm}^2}{0.62 \, \text{cm}} = 56.4516129 \, \text{cm} \approx 56.45 \, \text{cm}`

2.
`\frac{39 \, \text{g}}{24.2 \, \text{g}} = 1.611570248 \approx 1.61`

3.
`\frac{0.58 \, \text{dm}^3}{2.15 \, \text{dm}} = 0.2697674419 \, \text{dm}^2 \approx 0.27\, \text{dm}^2`

4.
`\frac{0.075 \, \text{g}}{0.003 \, \text{cm}^3} = 25 \, \text{g/cm}^3`