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Rounding to significant figures
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Foundational skills
Count sf in an integer
\[ 4070 \rightarrow 3 \text{ sf} \]
Count the number of significant figures in a whole number.
Count sf in a decimal
\[ 0.03040 \rightarrow 4 \text{ sf} \]
Count the number of significant figures in a decimal number.
Identify the Nth significant figure (>1)
\[ 30.045 \rightarrow \text{2nd is } 0 \]
Identify the Nth significant figure for numbers greater than 1.
Identify the Nth significant figure (<1)
\[ 0.004073 \rightarrow \text{3rd is } 7 \]
Identify the Nth significant figure for numbers less than 1.
Identify the decision digit (>1)
\[ 4728 \text{ to 2sf: } 2? \]
Identify the decision digit in numbers greater than 1.
Identify the decision digit (<1)
\[ 0.0304 \text{ to 1sf: } 0? \]
Identify the decision digit in numbers less than 1.
Rounding to 1 sf
Two-digit integers
\[ 47 \rightarrow 50 \]
Round a two-digit integer to 1 significant figure.
Three-digit integers
\[ 473 \rightarrow 500 \]
Round a three-digit integer to 1 significant figure.
Larger integers
\[ 4{,}736 \rightarrow 5{,}000 \]
Round an integer with 4 or more digits to 1 significant figure.
Integers with cascade to extra digit
\[ 96 \rightarrow 100 \]
Round an integer to 1 significant figure where it cascades.
Decimals greater than or equal to 1
\[ 34.72 \rightarrow 30 \]
Round a decimal number greater than or equal to 1 to 1 significant figure.
Decimals >=1 with cascade
\[ 9.47 \rightarrow 10 \]
Round a decimal to 1 significant figure where it cascades.
Numbers less than 1
\[ 0.0456 \rightarrow 0.05 \]
Round a number less than 1 to 1 significant figure.
Numbers less than 1 with cascade
\[ 0.096 \rightarrow 0.1 \]
Round a number less than 1 to 1 significant figure where it cascades.
Rounding to 2 sf
Three-digit integers
\[ 473 \rightarrow 470 \]
Round a three-digit integer to 2 significant figures.
Larger integers
\[ 4{,}736 \rightarrow 4{,}700 \]
Round an integer with 4 or more digits to 2 significant figures.
Integers with cascade at 2nd position
\[ 497 \rightarrow 500 \]
Round an integer to 2 significant figures where the second digit is 9.
Integers with cascade to extra digit
\[ 996 \rightarrow 1{,}000 \]
Round an integer to 2 significant figures where cascading adds a digit.
Decimals greater than or equal to 1
\[ 34.72 \rightarrow 35 \]
Round a decimal number greater than or equal to 1 to 2 significant figures.
Decimals >=1 with cascade
\[ 4.97 \rightarrow 5.0 \]
Round a decimal to 2 significant figures where the second digit is 9.
Decimals >=1 with cascade to extra whole digit
\[ 9.96 \rightarrow 10 \]
Round a decimal to 2 significant figures where cascading adds a whole digit.
Numbers less than 1
\[ 0.04567 \rightarrow 0.046 \]
Round a number less than 1 to 2 significant figures.
Numbers less than 1 with cascade
\[ 0.0498 \rightarrow 0.050 \]
Round a number less than 1 to 2 significant figures where it cascades.
Numbers less than 1 with cascade to fewer leading zeros
\[ 0.0987 \rightarrow 0.10 \]
Round less than 1 to 2 sf where cascade reduces leading zeros.
Rounding to 3 sf
Integers
\[ 4{,}736 \rightarrow 4{,}740 \]
Round an integer to 3 significant figures.
Integers with cascade at 3rd position
\[ 4{,}597 \rightarrow 4{,}600 \]
Round an integer to 3 significant figures where the 3rd digit is 9.
Integers with cascade to extra digit
\[ 9{,}996 \rightarrow 10{,}000 \]
Round an integer to 3 significant figures where cascading adds a digit.
Decimals greater than or equal to 1
\[ 34.567 \rightarrow 34.6 \]
Round a decimal >= 1 to 3 significant figures.
Decimals >=1 with cascade
\[ 34.97 \rightarrow 35.0 \]
Round a decimal to 3 significant figures where it cascades.
Numbers less than 1
\[ 0.045678 \rightarrow 0.0457 \]
Round a number less than 1 to 3 significant figures.
Numbers less than 1 with cascade
\[ 0.04598 \rightarrow 0.0460 \]
Round less than 1 to 3 sf where it cascades.
Special cases
Trailing zero required for precision
\[ 4.03 \rightarrow 4.0 \]
Round numbers where the answer must include a trailing zero.
Scientific notation for clarity
\[ 4700 \rightarrow 4.7 \times 10^3 \]
Express a number in scientific notation to clarify sf.
Reverse rounding numbers less than 1 (sf)
\[ \text{Which rounds to } 0.045? \]
Identify which numbers would round to a given target value.
Reverse rounding numbers greater than 1
\[ \text{Which rounds to } 450? \]
Identify which numbers would round to a given target value.
Multi-round Large Number
\[ 42756 \rightarrow \text{1, 2, 3 sf} \]
Round a large number to 1, 2, and 3 significant figures.
Multi-round Small Decimal
\[ 0.05362 \rightarrow \text{1, 2, 3 sf} \]
Round a small decimal to 1, 2, and 3 significant figures.
Timer (Optional)
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