Rounding to decimal places questions with answers

Questions

1. Question 1Nearest 10, 100, 1000 or whole number

   Write $12\,349$ correct to the nearest 1000.

   Show the worked solution

   1. Step 1: Keep up to the thousands digit: look at the next digitThe deciding digit is $3$.
   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, with zeros as place holders$12\,349 = 12\,000$ (nearest 1000)
2. Question 2Decimal places

   Write $45.678$ correct to 1 decimal place.

   Show the worked solution

   1. Step 1: Keep 1 decimal place: look at the next digitThe deciding digit is $7$.
   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, keeping every decimal place (even a 0)$45.678 = 45.7$ (1 d.p.)
3. Question 3Calculate, then round

   Use a calculator to evaluate $\dfrac{125}{13}$, giving your answer correct to 3 decimal places.

   Show the worked solution

   1. Step 1: Work it out on the calculator: write down at least 4 decimal places$\dfrac{125}{13} = 9.61538\ldots$
   2. Step 2: Round only at the end: look at the next digit; 5 or more rounds up$= 9.615$ (3 d.p.)
4. Question 4A longer expression, to 3 significant figures

   Use a calculator to evaluate $\dfrac{\sqrt[3]{100} + 3.4^{2}}{7.15 - 4.05}$, giving your answer correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Work out the numerator on its own (keep at least 4 decimal places)$\sqrt[3]{100} + 3.4^{2} = 16.2015\ldots$
   2. Step 2: Work out the denominator on its own$7.15 - 4.05 = 3.1$
   3. Step 3: Divide, using the full values (or put brackets round the top and the bottom on the calculator)$\dfrac{16.2015\ldots}{3.1} = 5.2263\ldots$
   4. Step 4: Round only at the end: keep 3 significant figures$= 5.23$ (3 s.f.)