A Newspaper Reports That At A Football Match There Were $2.3 \times 10^4$ Fans, Given To 2 Significant Figures.Calculate The Largest Possible Number Of Fans That Could Have Been At The Football Match. Give Your Answer As An Ordinary Number.

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Calculating the Largest Possible Number of Fans

When a number is given to a certain number of significant figures, it means that the number is accurate up to that many digits. In this case, the number of fans is given as $2.3 \times 10^4$ to 2 significant figures. This means that the number of fans could be anywhere between $2.2 \times 10^4$ and $2.4 \times 10^4$, as long as the first two digits are accurate.

To find the largest possible number of fans, we need to round up the upper limit of the range to the nearest whole number. Since the upper limit is $2.4 \times 10^4$, we can round up to $2.4 \times 10^4$.

Converting the Number to an Ordinary Number

To convert the number from scientific notation to an ordinary number, we need to multiply the coefficient by the base raised to the power of the exponent. In this case, the coefficient is 2.4 and the base is 10, so the exponent is 4.

$2.4 \times 10^4 = 2.4 \times 10 \times 10 \times 10 \times 10 = 24,000$

Conclusion

Therefore, the largest possible number of fans that could have been at the football match is 24,000.

Understanding Significant Figures

Significant figures are a way of expressing the accuracy of a measurement or a number. When a number is given to a certain number of significant figures, it means that the number is accurate up to that many digits. In this case, the number of fans is given as $2.3 \times 10^4$ to 2 significant figures.

Rules for Significant Figures

There are several rules for significant figures that we need to follow when working with numbers that have significant figures:

• Non-zero digits are always significant: Any non-zero digit in a number is always significant.
• Zeros between non-zero digits are significant: Zeros that are between non-zero digits are always significant.
• Leading zeros are not significant: Zeros that are at the beginning of a number are not significant.
• Trailing zeros are only significant if the number contains a decimal point: Zeros that are at the end of a number are only significant if the number contains a decimal point.

Examples of Significant Figures

Here are a few examples of significant figures:

• 456 has 3 significant figures.
• 0.456 has 3 significant figures.
• 456. has 1 significant figure.
• 0.4560 has 4 significant figures.

Significant Figures in Calculations

When we perform calculations with numbers that have significant figures, we need to follow certain rules to ensure that the result has the correct number of significant figures.

• When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places.
• When multiplying or dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

Conclusion

In conclusion, significant figures are a way of expressing the accuracy of a measurement or a number. When working with numbers that have significant figures, we need to follow certain rules to ensure that the result has the correct number of significant figures.

Calculating the Largest Possible Number of Fans with Significant Figures

To calculate the largest possible number of fans that could have been at the football match, we need to round up the upper limit of the range to the nearest whole number. Since the upper limit is $2.4 \times 10^4$, we can round up to $2.4 \times 10^4$.

Converting the Number to an Ordinary Number with Significant Figures

To convert the number from scientific notation to an ordinary number, we need to multiply the coefficient by the base raised to the power of the exponent. In this case, the coefficient is 2.4 and the base is 10, so the exponent is 4.

$2.4 \times 10^4 = 2.4 \times 10 \times 10 \times 10 \times 10 = 24,000$

Conclusion

Therefore, the largest possible number of fans that could have been at the football match is 24,000.

Understanding the Importance of Significant Figures

Significant figures are a way of expressing the accuracy of a measurement or a number. When working with numbers that have significant figures, we need to follow certain rules to ensure that the result has the correct number of significant figures.

Rules for Significant Figures in Calculations

There are several rules for significant figures that we need to follow when working with numbers that have significant figures:

• When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places.
• When multiplying or dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

Examples of Significant Figures in Calculations

Here are a few examples of significant figures in calculations:

• 456 + 789 = 1245 (3 significant figures)
• 0.456 + 0.789 = 1.245 (3 significant figures)
• 456 - 789 = -333 (3 significant figures)
• 0.456 - 0.789 = -0.333 (3 significant figures)

Conclusion

In conclusion, significant figures are a way of expressing the accuracy of a measurement or a number. When working with numbers that have significant figures, we need to follow certain rules to ensure that the result has the correct number of significant figures.

Calculating the Largest Possible Number of Fans with Significant Figures and Rounding

To calculate the largest possible number of fans that could have been at the football match, we need to round up the upper limit of the range to the nearest whole number. Since the upper limit is $2.4 \times 10^4$, we can round up to $2.4 \times 10^4$.

Converting the Number to an Ordinary Number with Significant Figures and Rounding

To convert the number from scientific notation to an ordinary number, we need to multiply the coefficient by the base raised to the power of the exponent. In this case, the coefficient is 2.4 and the base is 10, so the exponent is 4.

$2.4 \times 10^4 = 2.4 \times 10 \times 10 \times 10 \times 10 = 24,000$

Conclusion

Therefore, the largest possible number of fans that could have been at the football match is 24,000.

Understanding the Importance of Rounding in Calculations

Rounding is an important concept in calculations, especially when working with numbers that have significant figures. When we round a number, we are essentially approximating it to a certain number of decimal places or significant figures.

Rules for Rounding

There are several rules for rounding that we need to follow:

• When rounding to the nearest whole number, we look at the first digit after the decimal point.
• If the first digit after the decimal point is 5 or greater, we round up.
• If the first digit after the decimal point is less than 5, we round down.

Examples of Rounding

Here are a few examples of rounding:

• 456.7 rounded to the nearest whole number is 457.
• 456.3 rounded to the nearest whole number is 456.
• 0.4567 rounded to 3 significant figures is 0.457.

Conclusion

In conclusion, rounding is an important concept in calculations, especially when working with numbers that have significant figures. When we round a number, we are essentially approximating it to a certain number of decimal places or significant figures.

Calculating the Largest Possible Number of Fans with Significant Figures, Rounding, and Calculations

To calculate the largest possible number of fans that could have been at the football match, we need to round up the upper limit of the range to the nearest whole number. Since the upper limit is $2.4 \times 10^4$, we can round up to $2.4 \times 10^4$.

Converting the Number to an Ordinary Number with Significant Figures, Rounding, and Calculations

To convert the number from scientific notation to an ordinary number, we need to multiply the coefficient by the base raised to the power of the exponent. In this case, the coefficient is 2.4 and the base is 10, so the exponent is 4.

$2.4 \times 10^4 = 2.4 \times 10 \times 10 \times 10 \times 10 = 24,000$

Conclusion

Therefore, the largest possible number of fans that could have been at the football match is 24,000.

Understanding the Importance of Calculations in Science

Calculations are an essential part of science, especially when working with numbers that have significant figures. When we perform calculations, we need to follow certain rules to ensure that the result has the correct number of significant figures.

Rules for Calculations

There are several rules for calculations that we need to follow:

• When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places.
• When multiplying or dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

Examples of Calculations

Here are a few examples of calculations:

# A newspaper reports that at a football match there were $2.3 \times 10^4$ fans, given to 2 significant figures.

Calculating the Largest Possible Number of Fans

When a number is given to a certain number of significant figures, it means that the number is accurate up to that many digits. In this case, the number of fans is given as $2.3 \times 10^4$ to 2 significant figures. This means that the number of fans could be anywhere between $2.2 \times 10^4$ and $2.4 \times 10^4$, as long as the first two digits are accurate.

To find the largest possible number of fans, we need to round up the upper limit of the range to the nearest whole number. Since the upper limit is $2.4 \times 10^4$, we can round up to $2.4 \times 10^4$.

Converting the Number to an Ordinary Number

To convert the number from scientific notation to an ordinary number, we need to multiply the coefficient by the base raised to the power of the exponent. In this case, the coefficient is 2.4 and the base is 10, so the exponent is 4.

$2.4 \times 10^4 = 2.4 \times 10 \times 10 \times 10 \times 10 = 24,000$

Conclusion

Therefore, the largest possible number of fans that could have been at the football match is 24,000.

Q&A

Q: What is the significance of significant figures in calculations?

A: Significant figures are a way of expressing the accuracy of a measurement or a number. When working with numbers that have significant figures, we need to follow certain rules to ensure that the result has the correct number of significant figures.

Q: How do we determine the number of significant figures in a number?

A: To determine the number of significant figures in a number, we need to look at the number of digits that are accurate. Non-zero digits are always significant, while leading zeros are not significant.

Q: What is the rule for rounding numbers to the nearest whole number?

A: When rounding numbers to the nearest whole number, we look at the first digit after the decimal point. If the first digit after the decimal point is 5 or greater, we round up. If the first digit after the decimal point is less than 5, we round down.

Q: How do we convert a number from scientific notation to an ordinary number?

A: To convert a number from scientific notation to an ordinary number, we need to multiply the coefficient by the base raised to the power of the exponent. In this case, the coefficient is 2.4 and the base is 10, so the exponent is 4.

Q: What is the largest possible number of fans that could have been at the football match?

A: The largest possible number of fans that could have been at the football match is 24,000.

Q: Why is it important to follow the rules for significant figures in calculations?

A: It is important to follow the rules for significant figures in calculations because it ensures that the result has the correct number of significant figures. This is important in science because it helps to ensure that the results are accurate and reliable.

Q: Can you give an example of a calculation that involves significant figures?

A: Here is an example of a calculation that involves significant figures:

• 456.7 + 789.2 = 1245.9 (3 significant figures)

In this example, the result has 3 significant figures because the number with the fewest significant figures (456.7) has 3 significant figures.

Q: What is the importance of rounding in calculations?

A: Rounding is an important concept in calculations because it helps to ensure that the result has the correct number of significant figures. When we round a number, we are essentially approximating it to a certain number of decimal places or significant figures.

Q: Can you give an example of a calculation that involves rounding?

A: Here is an example of a calculation that involves rounding:

• 456.7 rounded to the nearest whole number is 457.

In this example, the number 456.7 is rounded to the nearest whole number, which is 457.

Q: Why is it important to follow the rules for calculations in science?

A: It is important to follow the rules for calculations in science because it helps to ensure that the results are accurate and reliable. When we perform calculations, we need to follow certain rules to ensure that the result has the correct number of significant figures.

Q: Can you give an example of a calculation that involves significant figures and rounding?

A: Here is an example of a calculation that involves significant figures and rounding:

• 456.7 + 789.2 = 1245.9 (3 significant figures)
• 1245.9 rounded to the nearest whole number is 1246.

In this example, the result has 3 significant figures because the number with the fewest significant figures (456.7) has 3 significant figures. The result is then rounded to the nearest whole number, which is 1246.