1.9.2 Estimation
Estimation:
Estimation is a way of approximately calculating a rough answer rather than the exact one.
In this process we round the numbers to something convenient.
Underestimated/Overestimated:
In addition of two numbers
If both numbers are rounded up then the answer will be overestimated
If both numbers are rounded down then the answer will be underestimated
Subtracting \( b \) from \( a \)
If \( b \) is rounded down and/or \( a \) is rounded up then the answer will be overestimated
If \( a \)is rounded up and/or \( b \) is rounded down then the answer will be underestimated
In multiplication of two numbers
If both numbers are rounded up then the answer will be overestimated
If both numbers are rounded down then the answer will be underestimated
Dividing \( a \) by \( b \)
If \( b \) is rounded down and/or \( a \) is rounded up then the answer will be overestimated
If \( a \) is rounded up and/or \( b \) is rounded up then the answer will be underestimated
Worked example:
\( 29 \) parcels each have a value of \( $ \ 68 \).
By writing each of these numbers correct to \( 1 \) significant figure,
find an estimate for the total value of these \( 29 \) parcels.
Write each number correct to \( 1 \) significant figure
\( 29 \)→\( 30 \)
\( 68 \)→ \( 70 \)
Perform calculation by using rounded numbers
\( 30\times 70=2100 \)
Estimate for the total value is \( $ \ 2100 \)
Without doing any calculation, complete this statement.
The actual total value of these \( 29 \) parcels is less than the answer to part (i) because
….Both numbers are rounded up…..