Round a calculated answer to the required accuracy

What you will learn

• Round a calculated answer to the required accuracy

Models used: number sentences, stories, tables.

Before you start

• Calculate a decimal quotient of whole numbers without a calculator

Find the nearest tenth

We want to round 0.36 to one decimal place. It lies between 0.3 and 0.4.

1. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   We want to round 0.36 to one decimal place. It lies between 0.3 and 0.4.

   One decimal place means tenths. So first find the two neighbouring tenths.

2. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   The halfway point is 0.35. Our number, 0.36, is just past it towards 0.4.

   Compare distances on the line: 0.36 is four hundredths from 0.4, but six hundredths from 0.3.

3. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   The closer tenth is 0.4. That is our rounded number.

   0.36 ≈ 0.4

   Rounding gives a nearby value at the precision requested. It does not mean 0.36 and 0.4 are exactly equal.

   What would happen at exactly 0.35?

   That is halfway. Using the usual rounding rule, we choose the higher tenth, 0.4.

Worked example: A new example, together

Calculate 46 ÷ 4, rounded to 1 decimal places.

1. Round only at the final step. Read each value with the heading above its column.

   Locate the requested place first, then its two neighbours and midpoint.

   Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

   Round only at the final step

   Unrounded value	Requested decimal places
   11.5000	1

2. Round only at the final step. Read each value with the heading above its column.

   Keep digits through the requested 1 decimal places.

   Round only at the final step

   Unrounded value	Requested decimal places
   11.5000	1

   Calculate 46 ÷ 4, rounded to 1 decimal places.

   11.5

3. Round only at the final step. Read each value with the heading above its column.

   Inspect the next digit: 5 or more rounds the retained value up.

   Round only at the final step

   Unrounded value	Requested decimal places
   11.5000	1

4. Round only at the final step. Read each value with the heading above its column.

   The rounded answer is 11.5.

   Round only at the final step

   Unrounded value	Requested decimal places
   11.5000	1

5. Round only at the final step. Read each value with the heading above its column.

   Check the result against the question we started with.

   Check neighbouring rounded values and the halfway point.

   We found 11.5. Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

   Round only at the final step

   Unrounded value	Requested decimal places
   11.5000	1

Common mistakes to discuss

• Rounding one digit at a time. Round once, from the digit in the next smaller place. 2.449 to one decimal place is 2.4; rounding the 9, then the 4, would wrongly give 2.5.

Check your understanding

• Round a calculated answer to the required accuracy
• justify decimal rounding at the requested accuracy
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.