Round measurements to decimal places

Measured length

\(\displaystyle 12.746\text{ m}\)

A measured length is 12.746 m. Which value records it to two decimal places?

Move the measurement from 4.321 to 4.329. Compare the original reading with its value rounded to two decimal places

At which reading does the rounded value first become 4.33 m?

Count from the decimal point

Keep the requested number of decimal places and inspect the next digit. Keep trailing zeros when they state the requested precision

1. 1Locate the deciding digit For two decimal places, the third digit after the decimal point decides the rounding \(\displaystyle 12.746\longrightarrow 12.75\)
2. 2Carry across nines If increasing the last kept digit produces ten, carry into the preceding place \(\displaystyle 7.996\longrightarrow 8.00\text{ (2 d.p.)}\)

Measured capacity

\(\displaystyle 8.996\text{ L}\)

A container's measured capacity is 8.996 L. Record it to two decimal places

Inspect the third decimal digit and carry through both nines. Write both decimal places, including zeros

Measured thickness

\(\displaystyle 0.04738\text{ m}\)

A measured thickness is 0.04738 m. Record it to three decimal places

Count three digits after the point, including the zero