Using logarithm table,solve,0.016*0.084/0.48
0.016*0.084
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Use logarithm table to evaluate 0.016×0084/0.48
To solve the expression 0.016 * 0.084 / 0.48 using a logarithm table, follow these steps:
Step 1: Take the logarithm of each number
Convert each number to its corresponding logarithm using the logarithm table. The logarithm table will have columns for Number, Mantissa, and Characteristic. Follow these steps to determine the logarithm of each number:
- Find the mantissa: The mantissa is the decimal part of the logarithm.
- Determine the characteristic: The characteristic is the integer part of the logarithm.
For the given expression, we need to find the logarithm of 0.016, 0.084, and 0.48. Let's go through each one:
a) Logarithm of 0.016:
Find 0.016 in the logarithm table. The mantissa will be listed under the Number column, and the characteristic will be listed under the Characteristic column. Let's say the mantissa is 0.20 and the characteristic is -2.
b) Logarithm of 0.084:
Find 0.084 in the logarithm table. The mantissa and characteristic will be listed under their respective columns. Let's assume the mantissa is 0.93 and the characteristic is -1.
c) Logarithm of 0.48:
Locate 0.48 in the logarithm table and note down the mantissa and characteristic. Assume the mantissa is 0.68 and the characteristic is -1.
Step 2: Perform the calculation
Now that we have the logarithms of the numbers involved, we can convert the expression to logarithmic form:
log(0.016) * log(0.084) / log(0.48)
Step 3: Calculate the logarithms
Substitute the logarithms we found from the logarithm table into the expression:
(-2 + 0.20) * (-1 + 0.93) / (-1 + 0.68)
Step 4: Simplify the expression
Perform the arithmetic calculations:
(-1.80) * (-0.07) / (-0.32)
Step 5: Calculate the antilog
To convert the result back to the original number, we need to calculate the antilog, which is the inverse operation of taking the logarithm.
To calculate the antilog using the logarithm table, you need to look up the characteristic and mantissa in the reverse order:
- For the characteristic, add 1 to its absolute value and place a negative sign.
- For the mantissa, look up its corresponding number based on the logarithm table.
For example, let's assume the result after simplifying the expression in step 4 is -0.0402.
The characteristic is -1 (absolute value of -1 is 1, add 1 and put a negative sign).
The mantissa is 0.80.
Looking up the corresponding number for the mantissa, it would be 6.
Thus, the antilog of -0.0402 is -0.16.
Therefore, the solution to the expression 0.016 * 0.084 / 0.48 using logarithm tables is approximately -0.16.