Round to the nearest tenth with decimals

Your student comes home with 0.96 and a red-ink instruction: "Round to the nearest tenth." The answer is 1.0, not 0.9, and the carry is what trips most fifth graders. This rule provides the rule and worked examples for each decimal place, then handles the carry edge cases and the specific question of rounding money to the nearest cent. Common Core standard 5.NBT.A.4 requires you to "use place value understanding to round decimals to any place," which is what these examples deliver.

Rounding is the deliberate replacement of a number with a nearby, simpler number. The method taught in US K-12 schools is "round half up": look at the digit immediately after the target place, and if that digit is 5 or higher, increase the target digit by one. For digits 0 through 4, leave the target digit unchanged. That is the rule you will apply in every example below.

Before you can round to a place, you have to find the place. The decimal point separates the whole-number part (left) from the fractional part (right). The first digit after the decimal point is the tenths place. The second is the hundredths place. The third is the thousandths place. The pattern continues: ten-thousandths, hundred-thousandths, millionths.

A place-value chart makes this concrete. Write 3.456 in a chart:

To round to the nearest tenth, look at the hundredths digit (the second digit after the decimal point). If that digit is 5 or more, increase the tenths digit by one. If it is 4 or less, keep the tenths digit as it is. Drop all digits after the tenths place.

Examples:

• 0.72: hundredths digit is 2 (less than 5) → 0.7
• 0.78: hundredths digit is 8 (5 or more) → 0.8
• 0.96: hundredths digit is 6 (5 or more) → tenths digit 9 increases to 10, which carries to the ones place → 1.0
• 2.34: hundredths digit is 4 → 2.3
• 2.39: hundredths digit is 9 → 2.4

The carry in the third example is where most errors happen. 0.96 rounded to the nearest tenth gives 1.0, not 0.9. Write the zero after the decimal point to show that the result is accurate to the tenths place.

Rounding to the nearest hundredth is the same operation as rounding to 2 decimal places. Look at the thousandths digit (the third digit after the decimal point). Apply the same rule: 5 or more rounds the hundredths digit up; 4 or less leaves it alone.

Examples:

• 0.573: thousandths digit is 3 (less than 5) → 0.57
• 0.578: thousandths digit is 8 (5 or more) → 0.58
• 0.995: thousandths digit is 5 → hundredths digit 9 increases to 10, which carries to the tenths place → 1.00
• 3.14159: thousandths digit is 1 → 3.14
• 3.14159 rounded to 2 decimal places: thousandths digit is 1 → 3.14

The last example is the classic approximation of pi. Note that rounding to 2 decimal places and rounding to the nearest hundredth are identical: both require you to examine the third decimal digit. The only difference is phrasing, a common exam question says "round to 2 decimal places" when it means round to the nearest hundredth.

Rounding to the nearest thousandth follows the same pattern but uses the fourth decimal digit, the ten-thousandths place. Look at that digit. If it is 5 or more, increase the thousandths digit by one. If it is 4 or less, leave the thousandths digit unchanged.

Examples:

• 0.1234: ten-thousandths digit is 4 (less than 5) → 0.123
• 0.1235: ten-thousandths digit is 5 (5 or more) → 0.124
• 0.9999: ten-thousandths digit is 9 → thousandths digit 9 increases to 10, which carries through the hundredths and tenths places → 1.000
• 0.4567: ten-thousandths digit is 7 → 0.457
• 0.4564: ten-thousandths digit is 4 → 0.456

The carry example for 0.9999 is extreme but instructive. Each time the digit in the target place is 9 and the next digit is 5 or higher, the rounding propagates left until it reaches a digit that is not 9. […] "

The carry is the single most common failure mode in rounding decimals. When the target digit is 9 and the digit to its right is 5 or higher, you cannot just add 1, you have to carry to the next place to the left. The rule does not change; the implementation is just more steps.

Take 0.96 to the nearest tenth. The tenths digit is 9. The hundredths digit is 6, which is 5 or more, so you need to increase the tenths digit by one. 9 + 1 = 10, so you write 0 in the tenths place and add 1 to the ones place. The result is 1.0.

Other carry examples with the same principle:

• 0.97 to the nearest tenth → 1.0
• 0.99 to the nearest tenth → 1.0
• 3.98 to the nearest tenth → 4.0
• 2.95 to the nearest tenth → 3.0
• 4.99 to the nearest tenth → 5.0

Each one follows the same two-step process: add 1 to the target digit, then propagate the carry leftward through any subsequent 9s. The answer always includes the zero in the tenths place when the result lands on a whole number, because dropping the zero would hide the precision of the rounding.

Rounding money to the nearest cent means rounding to 2 decimal places, because a cent is one hundredth of a dollar. […] First, the carry across the decimal point: $9.999 rounds to $10.00, not $10.99. This is consistent with the rounding method taught in Common Core 5.NBT.A.4, but note that different jurisdictions may have their own legal rules for tax rounding; those are not covered here.

Try these on your own before checking the answers. The method is the same for every question: identify the target place, look at the next digit to the right, and apply the 5-or-more rule. […] If it is 5 or more, increase the tenths digit by one. […] Then drop all digits after the tenths place. […] Adding 1 to 9 gives 10, so you write a 0 in the tenths place and carry 1 to the ones place. […] If it is 5 or more, increase the hundredths digit by one. […] The answer should always have two decimal places to show the rounding precision.

Other methods exist, including round half to even (used by Python's round() function and IEEE 754 default) and round half away from zero (used by Excel's ROUND function). These methods differ only in how they handle numbers exactly halfway between two candidates.

A chart helps you see which digit controls the rounding for each target place.

Print the practice questions, have the student work through them on paper, then check each answer against the table. The single most common error is forgetting to carry when the target digit is 9, so watch for that in every problem. If the student consistently handles the carry cases correctly, they have mastered rounding decimals to any place.