Decimals explained for parents: reading, comparing and using them at home

Your fourth grader writes $0.45 next to $0.5 and says the first one is more money. The same child can order 45 and 5 without blinking, which is what makes decimals so frustrating to explain at the kitchen table. A decimal is one number, and the point tells you where the whole stops.

What a decimal is, in one sentence

A decimal is a number that uses the places to the right of a point to show parts of one whole. The digits keep the job they have in whole numbers: each place is worth one tenth of the place on its left. Ten hundredths make one tenth, the way ten dimes make one dollar.

Reading the places out loud once makes the pattern land. In 3.456, the 4 is 4 tenths, the 5 is 5 hundredths and the 6 is 6 thousandths. The US standards state the rule behind every one of those places: a digit in one place is worth 1/10 of what it represents in the place to its left.

The point marks the whole, and it is not a separator between two numbers

Children often read 3.45 as "three point forty-five", as if 3 and 45 were two numbers stuck together. The size of the digits after the point depends on how many places there are, which is why 3.45 and 3.450 are equal while 3.45 and 3.045 are far apart.

The fix is to say the place name every time. Read 3.45 as "three and forty-five hundredths" and 3.045 as "three and forty-five thousandths", and the difference is audible. A round of place value practice makes the naming automatic.

Why decimals confuse children who are fine with whole numbers

Decimals break the one rule children trust most about numbers: more digits means a bigger number. 45 beats 5, 100 beats 99, and every year of school up to grade 4 rewards that habit.

Decimals switch the rule off without warning, and the error is not a small minority one. Asked which of 0.274 and 0.83 is greater, most 5th and 6th graders chose 0.274, the longer numeral. On the 2004 National Assessment of Educational Progress, fewer than 30% of 17-year-olds correctly translated 0.029 as 29/1000.

"Longer means bigger" is the classic wrong rule

The longer-is-bigger rule survives because it works on whole numbers and on price tags over a dollar. It fails the moment the digits sit to the right of the point, where 0.45 is 45 hundredths and 0.5 is 50 hundredths. Ask your child whether they would rather have 45 cents or half a dollar, and the wrong rule collapses on its own.

A second wrong rule hides behind the first: some children decide that a longer decimal must be the smaller one, because smaller pieces sound smaller. Both rules are right about half the time, which is why they survive.

How to read and compare decimals, step by step

Reading a decimal correctly is most of the work of comparing one, because the place name carries the size. Work through these six steps with pencil and paper the first few times, then drop the writing.

1. Read the whole part first. In 12.35, the whole part is 12. Say "twelve and" and pause there.
2. Name the last place. Count the digits after the point: one is tenths, two is hundredths, three is thousandths. In 12.35 there are two, so the number is "twelve and thirty-five hundredths".
3. Line the decimal points up. Write the two numbers one under the other with the points in a single vertical column, so every place sits in its own column.
4. Pad the shorter one with zeros. 0.5 becomes 0.50, so both numbers have the same number of places. A zero added on the right of a decimal never changes its value.
5. Compare place by place, from the left. Tenths first: 5 tenths against 4 tenths. 0.50 wins at the first place, so 0.5 > 0.45 and nothing after that matters.
6. Check the result against money. Turn both numbers into cents: 50 against 45. When the money answer disagrees, the written work has a mistake in it.

The step most people skip: padding with zeros

Padding with zeros turns a guess into a method, and adults skip it because they no longer need it. Writing 0.5 as 0.50 puts a digit in the hundredths column, so there is something to compare against the 5 in 0.45. The federal What Works Clearinghouse practice guide suggests a diagnostic for exactly this: ask a child to order 0.2, 0.12 and 0.056 from smallest to largest.

The order is 0.056, 0.12, 0.2. A child who calls 0.056 the largest is reading 56 instead of 56 thousandths. Comparing whole numbers in a greater-than and less-than game first keeps the symbols from becoming a second problem.

Play free in your browserComparing NumbersK–Grade 1

Decimals, fractions and percentages side by side

Decimals, fractions and percentages are three ways of writing the same amount, and each one is easier for a different job. Three quarters of a pizza is 3/4, 0.75 and 75%, and your child meets all three forms by grade 5.

Which form to pick

Money and measurement want a decimal, because the places line up with dollars and cents and with the metric system. Exact parts want a fraction, since one third is 1/3 exactly while 0.333… never finishes. Comparison wants a percentage, because every percentage is out of the same 100.

Converting between the three forms is division and multiplication, nothing more. The fractions guide for parents covers the fraction half of this, and a few rounds of percentage practice cover the third.

Play free in your browserPercentagesGrade 5+

Everyday decimals worked out

Decimals are easier to teach with objects that already carry them than with a worksheet, because the reason for the second place is visible. Four places your child meets decimals every week are money, kitchen scales, stopwatches and the sign at the gas station.

Money, scales, stopwatches and the price of gas

Money is the best first model because one dollar is cut into exactly 100 equal cents. $0.45 is 45 of those cents and $0.50 is 50 of them, so the second digit is a thing your child can count out in coins. Ask for $1.05 in coins and the zero in the tenths place stops looking like decoration.

• Kitchen scales. A scale reading 0.25 kg is showing 250 g, because a kilogram holds 1000 g and 0.25 is 25 hundredths of it.
• Stopwatches. A time of 12.35 seconds is faster than 12.4 seconds, because 12.4 is 12.40. This is the longer-is-bigger error with a result a child cares about.
• Gas prices. The sign reads 3.499 dollars a gallon, written to thousandths so the price can end in nine tenths of a cent. Rounded to the cent, that is 3.50 dollars.
• Recipes. A recipe calling for 1.5 cups wants one and a half cups, because 0.5 is 5 tenths of a cup.

Ten minutes at the grocery store covers more decimal place value than a page of exercises. A mixed set such as the math game for 5th graders keeps the written form current between trips.

How to check your child has decimals

Two short questions tell you whether your child understands decimals or is copying a procedure. Ask them on separate days, and listen to the reasoning rather than marking the answer.

The signals worth listening for

Watching how a child reaches an answer is more informative than the answer itself, because a wrong method often produces a right result.

• The 0.45 against 0.5 test: ask which is more money. A child who answers 0.5 and explains it as 50 cents has the place value. A child who answers 0.5 because "you add a zero" has the rule without the reason.
• The fraction test: ask what 0.7 is as a fraction. The answer is 7/10, and 0.07 is 7/100, which shows whether the place names are attached to sizes.
• The number line test: draw a line from 0 to 1 marked in tenths and ask where 0.45 goes. The practice guide reports that number lines divided into tenths made 5th and 6th graders more accurate at placing decimals.
• The reading test: write 3.07 and ask your child to read it aloud. The correct reading is "three and seven hundredths", and "three point seven" means the zero has been dropped.
• The estimate test: ask roughly what 0.8 × 0.9 comes to before any calculating. Both numbers are under 1 and fairly close to it, so the answer is 0.72, and the estimate rules out 0.072 and 7.2.

Common decimal mistakes, and your home checklist

Five mistakes cover most of the decimal work that comes home marked wrong. Each one has a one-line fix you can use at the kitchen table tonight.

• Longer means bigger. Calling 0.45 bigger than 0.5 treats the digits as a whole number. Pad the short one to 0.50 and compare the tenths first.
• Reading 3.07 as "three point seven". Skipping the zero loses a whole place and turns 7 hundredths into 7 tenths. Say the place name of the last digit every time.
• Dropping the zero in 0.5. Writing .5 makes the point easy to miss on a crowded page, and both the NIST style rules and the SI Brochure require the leading zero.
• Adding without lining up the point. Right-aligning 3.2 and 0.45 adds 2 tenths to 5 hundredths. Write 3.20 + 0.45 = 3.65 with the points in one column.
• Rounding twice. Rounding 4.649 to the cent gives 4.65, and rounding that again to one place gives 4.7, while 4.649 to one place is 4.6. Round once, from the original number.

A few rounds of a rounding game clear the last one faster than a rule sheet. Five habits keep the others from returning.

• Say it, do not point at it. Your child reads every decimal aloud with the place name before working with it.
• Zeros in place. Every number under 1 is written with its leading zero, and short decimals are padded before any comparison.
• Money check. Every answer in dollars is checked a second time in cents.
• Estimate first. Your child says roughly what the answer will be before multiplying or dividing decimals.
• One written page a week. A mixed worksheet for 5th graders keeps the written method current without a nightly fight.

The US standards set the timetable: decimal notation for fractions with denominators 10 or 100 in grade 4 (4.NF.C.6), comparing decimals to hundredths the same year (4.NF.C.7), then thousandths (5.NBT.A.3), rounding (5.NBT.A.4) and all four operations to hundredths in grade 5 (5.NBT.B.7). One fact is worth telling a child who reads foreign labels: many countries write a decimal comma where the US writes a point, and the SI Brochure permits either marker.