Rounding & Estimation Flashcards

All 7 cards in this deck

What are the steps to round a number to a given number of significant figures?

e.g. write $7357$ correct to 3 significant figures

1. Count significant figures from the first non-zero digit: $7, 3, 5$
2. Look at the next digit ($7$): 5 or more, so round up
3. Fill with zeros to keep the place value: $7360$

Which digit is the first significant figure of $0.00408$?

$4$ — the first non-zero digit.

What are the steps to work out an estimate for a calculation?

e.g. estimate $513 \times 0.81$

1. Round each number to 1 significant figure: $500$ and $0.8$
2. Do the easier calculation: $500 \times 0.8$
3. State the estimate: $\approx 400$

How do you estimate a square root that is not exact?

e.g. estimate $\sqrt{80}$

Round to the nearest square number: $\sqrt{81}=9$, so $\sqrt{80}\approx 9$.

True or false? When estimating a division, rounding the number you are dividing by down makes the estimate smaller.

False. Dividing by a smaller number gives a larger answer, so it makes the estimate bigger (an over-estimate).

In an estimate, both numbers in a multiplication are rounded up to 1 significant figure. Is the estimate an over-estimate or an under-estimate?

e.g. $513 \times 0.81 \approx 600 \times 0.9$

An over-estimate.
Both factors are larger than the true values, so the product is larger.

True or false? When estimating a division, rounding the number being divided up and rounding the number you are dividing by down gives an over-estimate.

True.
A larger number divided by a smaller number gives a bigger answer.