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Comparing decimals: align places before deciding

About 5 min

Questions stay in the language in which they were published.

These questions ask you to compare, order or locate decimals, sometimes in a context where smaller means earlier or faster. Written length is not a measure of size, so make the place values visible before choosing a direction.

Align, compare and check the context

Place decimal points in one vertical line and append trailing zeros until the numbers have the same number of decimal places. Compare whole-number parts first, then tenths, hundredths and thousandths. Stop at the first unequal column: that column decides the order. For example, compare 3.58 with 3.604 by writing 3.580 and 3.604. The tenths match, but 8 hundredths is greater than 0 hundredths, so 3.58 is greater.

Question signalMethod
Ascending or descending orderAlign every value, compare from the left, then arrange from least to greatest or greatest to least as requested.
Strictly betweenCheck both inequalities; equality with either endpoint is outside the open interval.
Exactly halfwaySubtract to find the gap, divide the gap by two, then add that half-gap to the lower endpoint. Between 1.2 and 1.6, the gap is 0.4 and the midpoint is 1.4.
Next value on a fixed-step displayAdd exactly one stated step; do not merely write any greater decimal.
Closest valueFind the absolute distance from the target and choose the smallest distance.

Avoid these comparison traps

Tempting routeHow to reject it
Call the decimal with more written digits greaterTrailing length says nothing about size. Align places and let the first unequal column decide.
Always call the shorter decimal greaterThat reverses the same faulty shortcut. Padding may reveal a later nonzero digit that makes the longer notation greater.
Include an endpoint in a strict intervalA strict inequality excludes equality. Pad the endpoint with zeros to expose an apparently different spelling of the same value.
Ignore what the ordered quantity meansNumerical order stays the same, but words such as fastest may require the smallest time to come first. Translate the context before arranging the values.
Choose the value whose digits look most like the targetMatching digit shapes or order does not measure closeness. Subtract and compare absolute distances.

Try it

Question 14

Enter the decimal exactly halfway between 2.35 and 2.37.

Question 19

A display advances in steps of 0.01. Enter the first value it shows after 3.49.

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Comparing decimals: align places before deciding · Questena