Question:
If $Log_{10}7=0.8451$ then the position of the first significant figure of $7^{-20}$ is
If $Log_{10}7=0.8451$ then the position of the first significant figure of $7^{-20}$ is
Updated On: May 14, 2024
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The Correct Option is B
Solution and Explanation
Let $x=7^{-20}$
$\log _{10} x=-20 \log _{10} 7$
$=-20(0.8451)$
$=-16.902$
Hence, the first significant figure is $17 .$
$\log _{10} x=-20 \log _{10} 7$
$=-20(0.8451)$
$=-16.902$
Hence, the first significant figure is $17 .$
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Concepts Used:
Significant Figures
The significant figures of a given number are those significant or important digits, which convey the meaning according to its accuracy. For example, 6.658 has four significant digits. These substantial figures provide precision to the numbers. They are also termed as significant digits.
Rules for Significant Figures:
- All non-zero digits are significant. 198745 contains six significant digits.
- All zeros that occur between any two non zero digits are significant. For example, 108.0097 contains seven significant digits.
- All zeros that are on the right of a decimal point and also to the left of a non-zero digit is never significant. For example, 0.00798 contained three significant digits.
- All zeros that are on the right of a decimal point are significant, only if, a non-zero digit does not follow them. For example, 20.00 contains four significant digits.
- All the zeros that are on the right of the last non-zero digit, after the decimal point, are significant. For example, 0.0079800 contains five significant digits.
- All the zeros that are on the right of the last non-zero digit are significant if they come from a measurement. For example, 1090 m contains four significant digits.