Answer :
To find the positions of the given numbers on a number line with a logarithmic scale (base 10), we need to determine the base 10 logarithm (log base 10) of each number. A logarithmic scale helps to represent values across a large range more evenly.
Here's a step-by-step guide on how to determine their placement:
1. Understand Logarithms: A logarithm with base 10 (log10) is the power to which 10 must be raised to obtain the number. This is helpful on a logarithmic scale as it compresses large ranges of numbers into manageable sections.
2. Calculate Each Logarithm:
- For 0.002: The log10 of 0.002 is approximately -2.70. This negative value shows that 0.002 is a small fraction.
- For 0.01: The log10 of 0.01 is -2. This would appear as the point corresponding to 10 raised to the power of -2.
- For 5: The log10 of 5 is about 0.70.
- For 7: The log10 of 7 is approximately 0.85.
- For 30: The log10 of 30 is approximately 1.47.
- For 50: The log10 of 50 is approximately 1.70.
- For 2000: The log10 of 2000 is approximately 3.30.
- For 6000: The log10 of 6000 is approximately 3.78.
- For 60000: The log10 of 60000 is approximately 4.78.
3. Plot on a Number Line:
- Since the number line is on a logarithmic scale, each whole number step in the log value represents a tenfold increase in the actual number.
- Numbers with lower log values such as -2.70 (for 0.002) will be placed to the far left, and higher log values like 4.78 (for 60000) will be placed far right on the logarithmic scale.
Now, you should match these log values with the appropriate positions on the logarithmic number line from the given options. Look for a line that spaces these log values from -2.70 to 4.78 at a constant interval, reflecting the properties of a logarithmic scale.
Here's a step-by-step guide on how to determine their placement:
1. Understand Logarithms: A logarithm with base 10 (log10) is the power to which 10 must be raised to obtain the number. This is helpful on a logarithmic scale as it compresses large ranges of numbers into manageable sections.
2. Calculate Each Logarithm:
- For 0.002: The log10 of 0.002 is approximately -2.70. This negative value shows that 0.002 is a small fraction.
- For 0.01: The log10 of 0.01 is -2. This would appear as the point corresponding to 10 raised to the power of -2.
- For 5: The log10 of 5 is about 0.70.
- For 7: The log10 of 7 is approximately 0.85.
- For 30: The log10 of 30 is approximately 1.47.
- For 50: The log10 of 50 is approximately 1.70.
- For 2000: The log10 of 2000 is approximately 3.30.
- For 6000: The log10 of 6000 is approximately 3.78.
- For 60000: The log10 of 60000 is approximately 4.78.
3. Plot on a Number Line:
- Since the number line is on a logarithmic scale, each whole number step in the log value represents a tenfold increase in the actual number.
- Numbers with lower log values such as -2.70 (for 0.002) will be placed to the far left, and higher log values like 4.78 (for 60000) will be placed far right on the logarithmic scale.
Now, you should match these log values with the appropriate positions on the logarithmic number line from the given options. Look for a line that spaces these log values from -2.70 to 4.78 at a constant interval, reflecting the properties of a logarithmic scale.
