Significant figures questions with answers

Questions

1. Question 1Whole numbers

   Write $74\,962$ correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Count 3 significant figures from the first non-zero digit, then look at the next digitThe 4th significant figure is $6$.
   2. Step 2: 5 or more: round up. 4 or less: round downIt is 5 or more, so round up.
   3. Step 3: Write the rounded number: fill the places up to the decimal point with zeros$74\,962 = 75\,000$ (3 s.f.)
2. Question 2Decimals greater than 1

   Write $99.95$ correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Count 3 significant figures from the first non-zero digit, then look at the next digitThe 4th significant figure is $5$.
   2. Step 2: 5 or more: round up. 4 or less: round downIt is 5 or more, so round up.
   3. Step 3: Write the rounded number: fill the places up to the decimal point with zeros$99.95 = 100$ (3 s.f.)
3. Question 3Small decimals (leading zeros)

   Write $0.08004$ correct to 2 significant figures.

   Show the worked solution

   1. Step 1: Count 2 significant figures from the first non-zero digit, then look at the next digitThe 3rd significant figure is $0$.
   2. Step 2: 5 or more: round up. 4 or less: round downIt is 4 or less, so round down.
   3. Step 3: Write the rounded number: keep a zero at the end if it is one of the significant figures$0.08004 = 0.080$ (2 s.f.)
4. Question 4How many significant figures?

   State the number of significant figures in $0.10$.

   Show the worked solution

   1. Step 1: Start counting at the first non-zero digitThe zeros before the first non-zero digit only show the place value: they are not significant.
   2. Step 2: Decide which of the zeros are significantA zero at the end of a decimal is significant: it shows the accuracy.
   3. Step 3: Count the significant figures$0.10$ has $2$ significant figures.