--- title: "Rounding decimals" subtitle: "Number Foundations · Place value and estimating · Lesson 18" --- # Rounding decimals **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A stopwatch says 12.846 seconds. Do you report 12.846, 12.85, 12.8 or 13? It depends who is asking, and what the timer can really measure. :::teacher-note **In one sentence:** Students round decimals on a number line to a given number of decimal places, then choose how much to round for a context such as time, money, tins of paint and a ruler's accuracy (AC9M7N05, nodes 1 and 2). **Students should be able to say:** I can round a decimal to a number of decimal places. I can say which digit decides, and why halfway rounds up. I can choose how much to round for the job, and explain my choice. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Which two numbers with 2 decimal places is 3.746 between? :::keep-together **Round 3.746 to 2 decimal places.** ☐ 3.7 ☐ 3.74 ☐ 3.75 ☐ 3.8 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 3.75. The digit after the hundredths is 6, so the 4 goes up to 5. 3.74 cuts the digits off. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## One digit decides :::keep-together ### Round it **Round 8.372 to 1 decimal place.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 8.4 The digit after the tenths is 7, so round up: 8.4. ::: :::keep-together ### Find the mistake **Kai rounds 2.349 to 1 decimal place. Click the line where the working goes wrong.** ``` 1 Round 2.349 to 1 decimal place. 2 The 9 rounds the 4 up: 2.349 is about 2.35. 3 The 5 rounds the 3 up: 2.35 is about 2.4. 4 Answer: 2.4 ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: only the digit straight after the tenths matters, and that is 4, so round down. Kai let the 9 push the 4 up, then rounded again. 2.349 to 1 decimal place is 2.3. ::: :::keep-together ### Halfway **Round 6.45 to 1 decimal place.** ☐ 6.0 ☐ 6.4 ☐ 6.45 ☐ 6.5 ::: :::teacher-note **Answer:** 6.5 The next digit is 5, exactly halfway, and halfway rounds up: 6.5. ::: :::typical ## How much is enough? **The stopwatch.** **Enough paint.** **Dollars and cents.** **The ruler.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Rounding :::keep-together ### Three places **Round 5.0763 to 3 decimal places.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 5.076 The digit after the thousandths is 3, so 5.076. ::: :::keep-together ### The 9 does not count **Round 7.0449 to 2 decimal places.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 7.04 The next digit is 4, so 7.04. ::: :::keep-together ### Share the bill **Three friends share a $50 bill: $50 ÷ 3 = 16.666… Each pays this much, to the nearest cent. (Write it as 16.xx.)** Answer: {{field-15}} ::: :::teacher-note **Answer:** 16.67 Cents are 2 decimal places. The next digit is 6, so 16.67. ::: :::keep-together ### Review: powers of 10 **Review: write $3 \times 10^2 + 5 \times 10^0$ as a number.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 305 300 + 5 = 305. The tens column is 0. ::: ## Make: lands on 4.57 Then find the smallest number you can that still rounds to 4.57. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A stick is measured as 83.46 cm with a ruler marked in millimetres. Round it sensibly, and say why.** {{lines-3}} ::: :::teacher-note **Answer:** 83.5 cm: the ruler shows millimetres, which is 1 decimal place of a centimetre. :::