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1 question has been asked in JEE-Main on this concept in last 10 years.
Generally, to calculate the number of significant figures in a number there are a set of rules that one has to memorize. So, let’s look into an alternate and easy way to do that.
Remember this!
1. The non-zero digits [1,2,3,4,5,6,7,8,9] are always significant.
2. Zero (0) may or may not be significant depending on its occurrence.
# Let’s classify different types of zero present in a term.
Leading zeros: Let’s call the zeros that are present before first non-zero digit as leading zeros.
Examples: 023, 00411, 0.0016 (the leading zeros are coloured), 0.08701 (here only first two zeros are leading zeros)
Trailing zeros: Let’s call the zeros that are present after the last non-zero digit as trailing zeros.
Examples: 340, 1100, 0.001600 (the trailing zeros are coloured), 1.40100(Here only last two zeros are trailing zeros)
Trapped zeros: Let’s call the zeros in between two non-zero digits as trapped zeros.
Examples: 2304, 30.04, 0.21007 (the trapped zeros are coloured)
Examples:
• 024 – This has only 2 S.F (significant figures), leading zeros are insignificant.
• 0.006 – This has only 1 SF.
• 0.123 – This has only 3 SF.
Examples:
• 1202 – This has 4 SF, trapped zero is significant.
• 12.021 – This has 5 SF.
Examples:
• 200 – This has only 1 SF, trailing zeros without decimal are insignificant.
• 20.0 – This has 3 SF, as decimal is present in the term, zeros are significant.
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• 10.800 – This has 5 SF, 1 trapped zero (always significant), 2 trailing zeros (significant) as decimal is present.
• 0.0020 – This has 2 SF, 3 leading zeros (always insignificant), 1 trailing zero (significant) as decimal is present.
• – This has 3 SF (1, 4, 5); is insignificant.
• 10.23 x 10^3 – This has 4 SF, here is insignificant.
• 30.00 – This has 4 SF, 3 trailing zeros (significant) as decimal is present.
• 10^5 has 1 significant figure only, as it can be written as or 100000…. which has only one significant figure.
Leading zeros: Let’s call the zeros that are present before first non-zero digit as leading zeros.
Examples: 023, 00411, 0.0016 (the leading zeros are coloured), 0.08701 (here only first two zeros are leading zeros)
Trailing zeros: Let’s call the zeros that are present after the last non-zero digit as trailing zeros.
Examples: 340, 1100, 0.001600 (the trailing zeros are coloured), 1.40100(Here only last two zeros are trailing zeros)
Trapped zeros: Let’s call the zeros in between two non-zero digits as trapped zeros.
Examples: 2304, 30.04, 0.21007 (the trapped zeros are coloured)
The Understanding:
Remember this!
1. Leading zeros are never significant.
Examples:
• 024 – This has only 2 S.F (significant figures), leading zeros are insignificant.
• 0.006 – This has only 1 SF.
• 0.123 – This has only 3 SF.
Did you know?
2. Trapped zeros are always significant.
Examples:
• 1202 – This has 4 SF, trapped zero is significant.
• 12.021 – This has 5 SF.
Remember this!
3. Trailing zeros are significant if decimal is present in the term, else they are insignificant.Examples:
• 200 – This has only 1 SF, trailing zeros without decimal are insignificant.
• 20.0 – This has 3 SF, as decimal is present in the term, zeros are significant.
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More examples:
• 10.800 – This has 5 SF, 1 trapped zero (always significant), 2 trailing zeros (significant) as decimal is present.
• 0.0020 – This has 2 SF, 3 leading zeros (always insignificant), 1 trailing zero (significant) as decimal is present.
• – This has 3 SF (1, 4, 5); is insignificant.
• 10.23 x 10^3 – This has 4 SF, here is insignificant.
• 30.00 – This has 4 SF, 3 trailing zeros (significant) as decimal is present.
• 10^5 has 1 significant figure only, as it can be written as or 100000…. which has only one significant figure.
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