ONE-EIGHTH STAGE 2025
St. Peter's SHS: 38 points
Osei Kyeretwie SHS: 38 points
Okuapemman School: 37 points
University Practice SHS: 43 points
Ghana SHS, Koforidua: 38 points
Winneba SHS: 30 points
Mawuli School: 48 points
Armed Forces SHTS: 38 points
Berekum Presby SHS: 33 points
ROUND 4 - TRUE OR FALSE
PREAMBLE
Determine the validity of the statements regarding significant figures.
1. The number $9450$ has four significant figures
ANSWER: FALSE
EXPLANATION:
It has 3 significant figures
2. The number $5008$ has four significant figures
ANSWER: TRUE
EXPLANATION:
Zeros between non-zero digits are significant, so $5008$ has $4$ significant figures.
3. The number 0.00534 has four significant figures
ANSWER: FALSE
EXPLANATION:
It has 3 significant figures
NOTES ON SIGNIFICANT FIGURES
Significant figures (or significant digits) indicate the precision of a measurement or calculated value.
They tell us which digits are reliable and which are simply placeholders.
Rules for Identifying Significant Figures:
1.
Non-zero digits are always significant.
Example: $457 \to 3$ significant figures.
Example: $25.34 \to 4$ significant figures.
2.
Zeros between non-zero digits are always significant (captive zeros).
Example: $1002 \to 4$ significant figures.
Example: $5.03 \to 3$ significant figures.
3.
Leading zeros are never significant; they only serve as placeholders.
Example: $0.0035 \to 2$ significant figures (3 and 5).
Example: $0.2 \to 1$ significant figure.
4.
Trailing zeros are significant only if the number contains a decimal point.
Example: $100 \to 1$ significant figure.
Example: $100.0 \to 4$ significant figures.
Example: $3.50 \to 3$ significant figures.
Rules for Calculations:
Addition and Subtraction – the final answer must have the same number of decimal places as the value with the fewest decimal places.
Example: $25.5+3.12$: $25.5 \to 1$ decimal place, $3.12 \to 2$ decimal places.
Raw sum: 28.62, rounded to 1 decimal place → 28.6
Multiplication and Division – the final answer must have the same number of significant figures as the value with the fewest significant figures.
Example: $2.4\times 12.12$: $2.4 \to 2$ significant figures, $12.12 \to 4$ significant figures.
Raw product: 29.088, rounded to 2 significant figures → 29
Exact Numbers: Counting numbers and defined constants have infinite significant figures and do not limit precision.
Examples: “12 eggs”, “3 people”, 1 inch = 2.54 cm (exact)
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PRACTICE QUESTIONS
PREAMBLE 1
The given number has three significant figures:
1. $0.0450$
ANSWER: TRUE
EXPLANATION:
Leading zeros do not count; the final zero after the decimal point does: $4$, $5$, $0$.
2. $3.07$
ANSWER: TRUE
EXPLANATION:
The zero between $3$ and $7$ counts.
3. $2500$
ANSWER: FALSE
EXPLANATION:
Trailing zeros of a whole number are not significant, so $2500$ has $2$ significant figures.
PREAMBLE 2
Rounded to $2$ significant figures:
1. $4.36 \to 4.4$
ANSWER: TRUE
EXPLANATION:
The third digit, $6$, rounds the $3$ up.
2. $0.08157 \to 0.082$
ANSWER: TRUE
EXPLANATION:
The significant digits start at $8$; the third one, $5$, rounds the $1$ up.
3. $6749 \to 6800$
ANSWER: FALSE
EXPLANATION:
The third digit, $4$, is less than $5$, so $6749 \to 6700$.
PREAMBLE 3
The given number has four significant figures:
1. $1.200$
ANSWER: TRUE
EXPLANATION:
Trailing zeros after a decimal point are significant.
2. $20.05$
ANSWER: TRUE
EXPLANATION:
The zeros between non-zero digits count, so all four digits are significant.
3. $0.0012$
ANSWER: FALSE
EXPLANATION:
Leading zeros do not count, so it has $2$ significant figures.