Grade 7 Decimals: Complete Guide to Decimal Operations & Conversions (US Standards)

GRADE 7 MATHEMATICS • LESSON 3

Grade 7 Decimals: Complete Guide to Decimal Operations & Conversions (US Standards)

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Understand place value, compare and round decimals, add, subtract, multiply & divide them — then take 15 exams with full step-by-step solutions.

What is a decimal?

Whole numbers count whole things: 1, 2, 3. But what about parts of a whole — like half a pizza or a price of three dollars and fifty cents? Decimals let us write those parts.

A decimal point separates the whole part from the part that is smaller than one. Everything to the left of the point is whole; everything to the right is a fraction of one.

Each step to the right is 10 times smaller: tenths, then hundredths, then thousandths. Use the explorer to see where every digit lives.

🔢 Place Value Explorer

Words you must know

Short, exact definitions to memorise.

Decimal
A number that uses a decimal point to show a value between two whole numbers.
Decimal point
The dot that separates the whole part (left) from the fractional part (right).
Place value
The value a digit has because of its position. Each place to the right is 10 times smaller.
Tenths / Hundredths / Thousandths
The first three places after the point: 1/10, 1/100, 1/1000.
Expanded form
A number written as the sum of each digit's value. Example: 3.14 = 3 + 0.1 + 0.04.
Terminating decimal
A decimal that ends. Example: 0.75.
Recurring decimal
A decimal where a digit (or group) repeats forever. Example: 0.333…

Decimals and fractions are the same family

Every terminating decimal is just a fraction with a denominator of 10, 100, 1000…

Examples: 0.7 = 7/10,   0.25 = 25/100 = 1/4,   0.5 = 5/10 = 1/2.

Working with decimals

This is your main study reference. Follow the numbered steps, copy the worked examples, and use the teacher hacks.

1) Comparing & ordering

  1. Compare the whole-number parts first. Bigger whole part wins.
  2. If the wholes match, compare the tenths, then hundredths, and so on.
Hack — even them out: give the numbers the same number of decimal places by adding zeros, then compare like whole numbers. 0.7 vs 0.65 → 0.70 vs 0.65 → 70 vs 65 → 0.7 is bigger.

2) Rounding

  1. Find the place you are rounding to (tenths, hundredths…).
  2. Look at the next digit to the right.
  3. If it is 5 or more, round up. If it is 4 or less, keep it the same.
  4. Drop the digits after the rounding place.
Round 3.47 to the nearest tenth
3.4|7 next digit is 7
7 is 5 or more, so round up
= 3.5
Hack: only the one digit right after the line decides. Ignore everything further right.

3) Adding & subtracting

  1. Write the numbers one above the other with the decimal points lined up.
  2. Fill any empty spaces with zeros so both have the same length.
  3. Add or subtract as usual.
  4. Bring the decimal point straight down into the answer.
Example: 2.5 + 1.75
2.50
+ 1.75
------
4.25
Hack — points in a column: the decimal points must form a straight vertical line. Pad with zeros so nothing is left blank.

4) Multiplying

  1. Ignore the decimal points and multiply the numbers as whole numbers.
  2. Count the total number of decimal places in both factors.
  3. Put that many decimal places in the answer.
Example: 0.3 × 0.4
3 × 4 = 12
1 + 1 = 2 decimal places
= 0.12
Hack — count, do not line up: for multiplying you do not line up the points. Just multiply, then count the places.

5) Dividing

  1. If the divisor (the number you divide by) is a decimal, move its point to make it a whole number.
  2. Move the point in the other number the same number of places.
  3. Divide as usual and bring the point straight up.
Example: 1.2 ÷ 0.4
move both points 1 place
= 12 ÷ 4
= 3
Hack — whole-number divisor: never divide by a decimal. Shift both points until the divisor is whole.

6) Decimal ↔ fraction

  1. The number of decimal places tells you the denominator: 1 place → over 10, 2 places → over 100, 3 places → over 1000.
  2. Write the digits over that denominator, then simplify.
Hack: count the decimal places, that is the number of zeros on the bottom. 0.7 = 7/10;   0.25 = 25/100 = 1/4.
🧮 Decimal Operations Lab

Test Yourself — 15 Exams

Each exam has 10 questions, and every answer comes with a step-by-step solution — even when you get it right.

Key takeaways

1. Each place after the point is 10 times smaller: tenths, hundredths, thousandths.

2. To compare, give them the same number of decimal places, then read like whole numbers.

3. To round, look at the next digit: 5 or more rounds up, 4 or less stays.

4. Add and subtract by lining up the points. Multiply by counting the decimal places.

5. To divide, make the divisor whole by moving both points the same amount.