Decimals to the Tenths and Hundredths (Kid Einsteins Class 13, Grades 3–4) — 8 Posters, Theory, 40 Practice Questions + 10 Word Problems with Hidden Answers

Theory — what a decimal is

A decimal is a number that uses a decimal point to show a whole number and parts of a whole. The digits to the left of the decimal point are whole numbers. The digits to the right of the decimal point are parts of a whole.

Decimals are built on the base-10 number system: just like the ones, tens, and hundreds places grow by ×10 to the left, the places to the right of the decimal point shrink by ÷10.

• The first place to the right of the decimal point is the tenths place. One tenth = 1/10 = 0.1.
• The second place to the right is the hundredths place. One hundredth = 1/100 = 0.01.

Example: in 4.37 the 4 is 4 ones, the 3 is 3 tenths, and the 7 is 7 hundredths. So 4.37 = 4 + 0.3 + 0.07.

Where decimals show up on the Upper West Side: money ($2.75 for a bagel), measurement (a 1.5 m desk), sports (a runner finishing 100 m in 9.8 seconds), science (98.6°F body temperature). If it needs to be precise, it uses a decimal.

Theory — tenths

A tenth is one of ten equal parts of a whole. When we divide something into 10 equal parts, each part is called a tenth and can be written as either a fraction or a decimal:

1/10  =  0.1

Ten tenths make one whole:

10/10 = 1     1.0 = 1     0.1 + 0.1 + … + 0.1 (10 times) = 1

More examples: 2/10 = 0.2, 3/10 = 0.3, 7/10 = 0.7, 9/10 = 0.9.

Pizza model: if you cut a pizza into 10 equal slices, one slice is one tenth (0.1) of the pizza. Three slices is three tenths (0.3). Ten slices is the whole pizza (1.0).

Theory — hundredths

A hundredth is one of one hundred equal parts of a whole. When we divide something into 100 equal parts, each part is a hundredth and can be written as either a fraction or a decimal:

1/100  =  0.01

The second digit to the right of the decimal point is the hundredths place. In 4.37:

• the 3 is in the tenths place (3 tenths = 0.3)
• the 7 is in the hundredths place (7 hundredths = 0.07)
• together, 0.37 means 37 hundredths

More examples: 25/100 = 0.25, 37/100 = 0.37, 8/100 = 0.08.

Watch out for 8/100. It is not 0.8. Eight hundredths must have a zero in the tenths place: 8/100 = 0.08. The zero is a placeholder that pushes the 8 into the hundredths place.

Theory — decimal place value and expanded form

Each digit in a decimal has a value based on its place. The place-value chart runs, from left of the decimal point outward:

Ones  .  Tenths   Hundredths

To find the value of a digit, multiply the digit by its place value:

• ones digit × 1
• tenths digit × 0.1
• hundredths digit × 0.01

Example — 3.47 in expanded form:

3.47 = 3×1 + 4×0.1 + 7×0.01 = 3 + 0.4 + 0.07

The zero rule. A zero in a decimal is not just decoration — it holds the place value. In 12.06 the 0 shows that there are 0 tenths, which is why the 6 is a hundredth, not a tenth. In 7.90 the trailing zero shows that we measured all the way to the hundredths and there were none there — 7.9 and 7.90 are equal in value but 7.90 signals more precise measurement.

Theory — reading and writing decimals in three forms

Every decimal can be written in three ways:

• Standard form — the digits with a decimal point (0.25).
• Word form — in English words (twenty-five hundredths).
• Fraction form — with denominator 10 or 100 (25/100).

How to read a decimal (3-step rule):

1. Read the whole-number part (the number before the decimal point).
2. Say “and” for the decimal point.
3. Read the decimal part as if it were a whole number, then say the place-value name of the last digit (tenths or hundredths).

Common mistake: reading 0.37 as “zero point three seven.” That is how people say it out loud in a hurry, but in a math class the answer we want is “thirty-seven hundredths” — because that is the answer that tells us the place value of the last digit.

Theory — comparing and ordering decimals

The 4-step compare rule — work left to right, place by place:

1. Compare the ones place. The bigger ones digit wins.
2. If the ones are equal, compare the tenths place.
3. If the tenths are also equal, compare the hundredths place.
4. You can also use a number line: numbers farther to the right are greater.

The classic trap: thinking 0.25 is bigger than 0.3 because “25 is bigger than 3.” Not true — the digits after the decimal point are not read as whole numbers.

Same-length trick. Give both decimals the same number of decimal places by adding zeros on the right (this does not change the value): 0.3 = 0.30, so 0.30 vs 0.25 is easy — 30 hundredths > 25 hundredths, so 0.3 > 0.25.

Ordering examples:

• Least to greatest: 0.05, 0.17, 0.21, 0.3  →  0.05 < 0.17 < 0.21 < 0.3
• Greatest to least: 1.2, 1.08, 1.05, 0.95  →  1.2 > 1.08 > 1.05 > 0.95

Theory — decimals on a number line

A number line shows numbers in order, with distance = value. To locate a decimal:

• Tenths: divide the distance from 0 to 1 into 10 equal jumps. Each jump is one tenth (0.1). 0.3 is 3 jumps to the right of 0.
• Hundredths: divide the distance from 0 to 1 into 100 equal jumps. Each jump is one hundredth (0.01). Or zoom in: divide the space between two tenths into 10 more equal jumps.
• Which is bigger? The number farther to the right is greater.

Examples:

Landmark trick. Half of 1 is 0.5. Quarter of 1 is 0.25. Three-quarters is 0.75. If you can place 0, 0.25, 0.5, 0.75, and 1 first, every other hundredth is easier.

Theory — decimals in real life

Money. Money is written with two decimal places because one cent is one hundredth of a dollar: $0.01 = 1¢. That is why every price tag on the Upper West Side is written to the hundredth.

Example: $2.75 = 2 whole dollars + 75 hundredths of a dollar = 2 dollars and 75 cents.

Measurement. When a length, weight, or volume is not a whole unit, we use a decimal to be more precise:

• A pencil that is 3.47 cm long is 3 whole centimeters and 47 hundredths of a centimeter.
• A bowl of strawberries that weighs 0.85 kg weighs 85 hundredths of a kilogram.
• A pitcher that holds 0.50 L holds 50 hundredths of a liter (which is half a liter).

Adding and subtracting decimals in a word problem: line up the decimal points and add or subtract as usual. A pen is $1.40 and a notebook is $3.25: total = $3.25 + $1.40 = $4.65. A ribbon 1.75 m long, cut 0.60 m: left = 1.75 − 0.60 = 1.15 m.

What are decimals to the tenths and hundredths, and when does my grade 3 or 4 child need them?

A decimal is a number that uses a decimal point to show a whole number and parts of a whole. The first digit to the right of the decimal point is the tenths place (one of ten equal parts of a whole; 0.1 = 1/10) and the second digit is the hundredths place (one of one hundred equal parts of a whole; 0.01 = 1/100). Most Upper West Side and Manhattan grade 3 students meet tenths through measurement and money; grade 4 makes tenths and hundredths fluent — reading them, writing them in words and fractions, placing them on a number line, and comparing them. Kid Einsteins Class 13 is the class where a grade 3–4 student stops guessing and starts reading a decimal the same way they read $2.75.

How do I read a decimal like 4.37?

Read the whole-number part first (four), then say “and” for the decimal point, then read the decimal part as if it were a whole number and finish with the place-value name of the last digit. 4.37 → “four and thirty-seven hundredths” because the last digit (7) is in the hundredths place. 4.3 → “four and three tenths” because the last digit (3) is in the tenths place. 0.05 → “five hundredths” (no whole part, and there is a 0 holding the tenths place). The place name of the last digit is the whole rule.

How do I compare decimals like 0.25 and 0.3?

Compare place by place from left to right — ones, then tenths, then hundredths. 0.25 vs 0.3: ones are equal (0 = 0), so compare tenths. 2 tenths vs 3 tenths → 3 tenths is greater, so 0.3 > 0.25. The classic grade 3–4 mistake is thinking 0.25 is bigger because “25 is more than 3.” That is wrong — the digits after the decimal point are NOT read as whole numbers. A useful trick: give both decimals the same number of decimal places by adding zeros on the right. 0.3 = 0.30, and now 0.30 vs 0.25 is easy: 30 hundredths > 25 hundredths.

How are decimals connected to fractions?

A decimal is just another way to write a fraction whose denominator is 10, 100, 1,000, and so on. 0.1 = 1/10, 0.3 = 3/10, 0.7 = 7/10. 0.01 = 1/100, 0.25 = 25/100, 0.68 = 68/100. This is the same idea Kid Einsteins used in Class 11 (adding fractions with like denominators) — a decimal is a fraction with an especially friendly denominator that lets us use place value instead of drawing bars.

How are decimals used in money and measurement?

Money uses two decimal places because one cent is one hundredth of a dollar (0.01 = 1¢). $2.75 means 2 dollars and 75 hundredths of a dollar = 2 dollars and 75 cents. Measurement uses decimals when a length is not a whole unit: a pencil that is 3.47 cm long is 3 whole centimeters plus 47 hundredths of a centimeter. Every grocery-store price tag, MetroCard balance, and metric ruler on the Upper West Side is decimal practice.

How do I place a decimal on a number line?

For tenths, divide the distance from 0 to 1 into 10 equal jumps — each jump is one tenth. 0.3 sits three jumps to the right of 0. For hundredths, divide the distance from 0 to 1 into 100 equal jumps — each jump is one hundredth — or zoom in between two tenths and divide that shorter distance into 10 more equal jumps. 0.47 sits between 0.4 and 0.5, closer to 0.5 (seven of the ten little jumps past 0.4). Numbers farther to the right are greater.

Why do some countries write a decimal comma instead of a decimal point?

The value is the same — the punctuation is different. Much of continental Europe and Latin America uses a comma as the decimal separator (3,5 = three and five tenths), while the United States, United Kingdom, and most of Asia use a decimal point (3.5). Great real-world example for grade 3–4 students: the mathematics of decimals is universal, even when the notation is not. On any American SHSAT, SAT, or Regents exam, use the decimal point.

How does SOMATH teach decimals to the tenths and hundredths?

In-person, in small groups of 4–8 grade 3–4 students, at 226 W 79th St on the Upper West Side. Every Kid Einsteins Class 13 session opens with the decimal place-value chart (ones, decimal point, tenths, hundredths), moves through tenths and hundredths grids, then reads and writes decimals in three forms (standard, word, fraction), then compares and orders, then places on a number line, and closes with real-life money and measurement word problems. Class 13 is the direct prerequisite for the fractions–decimals–percents bridge used in Pre-Algebra Class 7 (decimals four operations) and Pre-Algebra Class 10 (percent). Call (646) 668-6151 or book a free 30-minute evaluation.