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Approximations

8 min read

Why approximate?

Sometimes an exact number is too long or not needed. A road is "about 12 km", not 12.0374 km. An approximation is a number close to the exact one. Rounding off is the main way to make one.

Rounding off

Rounding on a number lineA number line from 3.40 to 3.50. The number 3.46 is closer to 3.50 than to 3.40, so it rounds to 3.5 to one decimal place. The halfway point 3.45 rounds up.3.403.453.503.46nearer to 3.5halfway
On the number line you can see which mark is nearer.
Try itRound a number

Choose a number and how many decimal places to keep. Compare the number with its rounded value on the number line.

Significant figures and estimating

Significant figures count from the first non-zero digit. 0.004 52 rounded to 2 significant figures is 0.0045. To estimate an answer, round each number to one significant figure first, then calculate.

Worked exampleEstimate a calculation

Estimate .

  1. Round each number to 1 significant figure: 48 → 50 and 21 → 20.
  2. Multiply.

Answer: The estimate is 1 000. The exact answer is 1 008, which is close.

Check yourself Round 6.849 to 1 decimal place.
Check yourself Round 12 560 to the nearest hundred.

Key terms

Approximation
A value close to, but not exactly, the true value.
Rounding
Replacing a number by a nearby simpler one.
Significant figure
A digit that carries meaning, counted from the first non-zero digit.

Summary

  • Look at the next digit: 5 or more rounds up, 4 or less stays.
  • Decimal places count after the point; significant figures count from the first non-zero digit.
  • Estimate by rounding to 1 significant figure first.
Units Geometry