What are decimals and how are they used in Mathematics?

Decimals are a way of representing fractions in a base-10 system, using a decimal point to separate the whole number from the fractional part. In Mathematics, especially in the IB MYP curriculum, decimals are used to express values that are not whole numbers, such as measurements, currency, and percentages, providing a precise way to handle non-integer numbers.

How do you convert a fraction to a decimal?

To convert a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number). For example, to convert 3/4 to a decimal, divide 3 by 4 to get 0.75. This method is commonly taught in the IB MYP Mathematics curriculum as it helps students understand the relationship between fractions and decimals.

What is the process for rounding decimals?

Rounding decimals involves adjusting the number to a specified place value. To round a decimal, look at the digit immediately to the right of the desired place value. If this digit is 5 or greater, increase the digit in the rounding place by one. If it is less than 5, leave the digit in the rounding place unchanged. This concept is crucial in Mathematics for simplifying numbers while maintaining accuracy.

How do you add and subtract decimals?

To add or subtract decimals, align the decimal points vertically and proceed as you would with whole numbers. Ensure each digit is in the correct place value column. After performing the addition or subtraction, place the decimal point in the result directly below the other decimal points. This method is emphasized in the IB MYP Mathematics curriculum to ensure accuracy in calculations involving decimals.

What are some common mistakes to avoid when working with decimals?

Common mistakes include misaligning decimal points during calculations, forgetting to add zeros as placeholders, and incorrectly rounding numbers. It's important to carefully align decimal points and understand place value to avoid these errors. The IB MYP Mathematics curriculum stresses the importance of precision and attention to detail when working with decimals.

Why is "Adding decimals as if they were whole numbers, right-aligned." a common mistake in Decimals?

Why it happens: Habit from integer addition. How to avoid it: Align DECIMAL POINTS (not the right-hand digits). Pad with zeros if needed.

Why is "Forgetting to count decimal places in the answer." a common mistake in Decimals?

Why it happens: After multiplying as integers, students stop. How to avoid it: Total d.p. in original numbers = d.p. in answer. 0.3 × 0.5 1.5; it's 0.15.

Why is "Counting leading zeros as significant figures." a common mistake in Decimals?

Why it happens: Habit of counting from the left. How to avoid it: Leading zeros are NEVER significant. 0.00427 has THREE s.f. (4, 2, 7).

NumberIB MYP Maths Extended Level

Decimals

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Decimals — IB MYP Mathematics (Extended): place value, operations and rounding

Decimals extend our number system into the rationals. This MYP Mathematics Extended note covers place value, the four operations, rounding, and the link to fractions.

What you’ll learn

Mapped to the IB MYP Mathematics subject guide (2026 onwards).

MYP Mathematics A — Identify place value to thousandths and beyond.
MYP Mathematics A — Apply the four operations to decimals.
MYP Mathematics A — Round to a given number of d.p. or s.f.
MYP Mathematics D — Use decimals in real contexts (money, measurement).

Place value

Each position is 10× the one to its right.

Every digit in a decimal has a PLACE VALUE — its position multiplies its size by a power of 10.

For the number $3.142$ :

Digit	Position	Place value
3	units	$3 \times 1 = 3$
1	tenths	$1 \times 0.1 = 0.1$
4	hundredths	$4 \times 0.01 = 0.04$
2	thousandths	$2 \times 0.001 = 0.002$

Total: $3 + 0.1 + 0.04 + 0.002 = 3.142$ .

The decimal point separates the units (and powers of 10) from the fractional parts. Each position is 10× the one to its right.

A useful exercise: write $0.073$ as a sum of place values. $0.073 = 0 \times 1 + 0 \times 0.1 + 7 \times 0.01 + 3 \times 0.001 = 0 + 0 + 0.07 + 0.003.$

Tenths $= 0.1$ , hundredths $= 0.01$ , thousandths $= 0.001$ .
Decimal point separates integer part from fractional part.
Each position is $10\times$ the position to its right.

Adding and subtracting decimals

Line up the decimal points.

Stack the numbers vertically with the decimal points aligned. Fill in zeros so all numbers have the same number of decimal places, then add/subtract digit by digit (carrying or borrowing as needed).

Worked example. $12.7 + 3.456$ .

   12.700
 +  3.456
 --------
   16.156

Subtraction worked example. $7.4 - 2.83$ .

   7.40
 - 2.83
 ------
   4.57

The most common mistake is starting from the wrong end. Always start from the RIGHT.

Line up the decimal points.
Add trailing zeros so all numbers have the same number of d.p.
Add/subtract from the RIGHT.

Multiplying and dividing decimals

Convert to integers temporarily, then place the point.

Multiplication. Ignore the decimal points and multiply as if both numbers were whole. Then COUNT the total number of decimal places in the original numbers and put that many in the answer.

Worked example. $0.4 \times 0.07$ .

Ignoring points: $4 \times 7 = 28$ .
Total decimal places: $1 + 2 = 3$ .
Place the point: $0.028$ .

Division. Convert the DIVISOR to a whole number by multiplying BOTH numbers by the same power of 10.

Worked example. $7.2 \div 0.3$ .

Multiply both by 10: $72 \div 3 = 24$ .

Worked example. $0.045 \div 0.5$ .

Multiply both by 10: $0.45 \div 5 = 0.09$ .

A common Extended-level trick: long division with decimals. If the divisor is already a whole number, just bring the decimal point straight up into the answer.

Multiplication: ignore points, multiply as integers, then count d.p.
Division: multiply both numbers by a power of 10 to make the divisor whole.
Place the point in the answer at the very end.

Rounding

Decimal places (d.p.) vs significant figures (s.f.).

Rounding to a number of DECIMAL PLACES (d.p.) — count digits AFTER the decimal point.

Worked example. Round $3.4567$ to:

1 d.p. $\to$ $3.5$ (look at the 5 after $3.4$ — round up).
2 d.p. $\to$ $3.46$ .
3 d.p. $\to$ $3.457$ .

Rounding to a number of SIGNIFICANT FIGURES (s.f.) — count all digits starting from the first non-zero one.

Worked example. Round $0.04567$ to:

1 s.f. $\to$ $0.05$ (first non-zero digit is the 4).
2 s.f. $\to$ $0.046$ .
3 s.f. $\to$ $0.0457$ .

Worked example. Round $7421$ to 2 s.f. — answer is $7400$ . The two 0s are placeholders, NOT significant.

Rule for rounding: look at the digit after the cut. If it's 5 or more, round up. If it's 4 or less, round down.

For Extended Level, also know:

Rounding to a specific PLACE (nearest 10, 100, 1000) is common in real-life contexts.
Truncating is NOT rounding — it just chops off digits. Avoid unless explicitly asked.

d.p. = positions AFTER the point.
s.f. = positions starting from the first non-zero digit.
5 or more $\to$ round up. 4 or less $\to$ round down.

How it’s examined

Criterion A: speedy non-calculator operations. Criterion C: clearly written calculations. Criterion D: money, measurement and estimation contexts.

Sources: IB MYP Mathematics subject guide (IBO, official). Last reviewed 2026-05-25.

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Step-by-step worked examples — Decimals

Step-by-step solutions to past-paper-style questions on decimals, written exactly the way a tutor would explain them at the board.

1Add decimals with different d.p.
Getting started• addition
Question
Calculate $14.6 + 0.87 + 3.5$ .
Step-by-step solution
1. Step 1
  Align decimal points and pad with zeros: $14.60$ , $0.87$ , $3.50$ .
2. Step 2
  Add from the right: $0 + 7 + 0 = 7$ .
3. Step 3
  $6 + 8 + 5 = 19$ , write 9 carry 1.
4. Step 4
  $4 + 0 + 3 + 1 = 8$ . $1 + 0 + 0 = 1$ . Result: $18.97$ .
Answer
$18.97$
2Multiply decimals
Building confidence• multiplication
Question
Calculate $0.6 \times 0.04$ .
Step-by-step solution
1. Step 1
  Multiply as integers (ignore points): $6 \times 4 = 24$ .
2. Step 2
  Count decimal places: $0.6$ has 1 d.p., $0.04$ has 2 d.p. Total $= 3$ .
3. Step 3
  Place the point so the answer has 3 d.p.: $0.024$ .
Answer
$0.024$
3Divide decimals
Building confidence• division
Question
Calculate $0.84 \div 0.04$ .
Step-by-step solution
1. Step 1
  Make the DIVISOR a whole number. Multiply both by $100$ : $84 \div 4$ .
2. Step 2
  $84 \div 4 = 21$ .
Answer
$21$
4Round to d.p. and s.f.
Stretch• rounding
Question
Round $0.04567$ to (a) 2 d.p. (b) 2 s.f. (c) 3 s.f.
Step-by-step solution
1. Step 1
  (a) 2 d.p.: count 2 digits after the point. $0.04567$ → look at 3rd digit (5) → round up → $0.05$ .
2. Step 2
  (b) 2 s.f.: first non-zero digit is the 4 (position 'hundredths'). Two s.f. take 4 and 5. Look at the next digit (6) — round up. $0.046$ .
3. Step 3
  (c) 3 s.f.: take digits 4, 5, 6. Look at the next digit (7) — round up. $0.0457$ .
Answer
(a) $0.05$ (b) $0.046$ (c) $0.0457$

Key Definitions and Keywords — Decimals

Definitions to memorise and the exact keywords mark schemes credit for decimals answers — sharpened from recent examiner reports for the 2026 IB MYP Mathematics (Extended) sitting.

Place value
Examiner keyword
The value of a digit determined by its position. Each position is 10× the one to its right.
Decimal place (d.p.)
Examiner keyword
A position to the right of the decimal point. $3.456$ has 3 d.p.
Significant figure (s.f.)
Examiner keyword
A digit that contributes to the precision of a number, starting from the first non-zero digit.
Truncate
Cut off digits without rounding. NOT the same as rounding.

Common Mistakes and Misconceptions — Decimals

The traps other students keep falling into on decimals questions — taken from recent IB MYP Mathematics (Extended) examiner reports and mark schemes — and how to avoid them.

✕Adding decimals as if they were whole numbers, right-aligned.
Why it happens
Habit from integer addition.
How to avoid it
Align DECIMAL POINTS (not the right-hand digits). Pad with zeros if needed.
✕Forgetting to count decimal places in the answer.
Why it happens
After multiplying as integers, students stop.
How to avoid it
Total d.p. in original numbers = d.p. in answer. $0.3 \times 0.5 \ne 1.5$ ; it's $0.15$ .
✕Counting leading zeros as significant figures.
Why it happens
Habit of counting from the left.
How to avoid it
Leading zeros are NEVER significant. $0.00427$ has THREE s.f. (4, 2, 7).

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

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Decimals — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Digit

Position

Place value

units

3 \times 1 = 3

tenths

1 \times 0.1 = 0.1

hundredths

4 \times 0.01 = 0.04

thousandths

2 \times 0.001 = 0.002

Rounding to a number of DECIMAL PLACES (d.p.) — count digits AFTER the decimal point.

Worked example. Round $3.4567$ to:

1 d.p. $\to$ $3.5$ (look at the 5 after $3.4$ — round up).
2 d.p. $\to$ $3.46$ .
3 d.p. $\to$ $3.457$ .

Rounding to a number of SIGNIFICANT FIGURES (s.f.) — count all digits starting from the first non-zero one.

Worked example. Round $0.04567$ to:

1 s.f. $\to$ $0.05$ (first non-zero digit is the 4).
2 s.f. $\to$ $0.046$ .
3 s.f. $\to$ $0.0457$ .

Worked example. Round $7421$ to 2 s.f. — answer is $7400$ . The two 0s are placeholders, NOT significant.

Rule for rounding: look at the digit after the cut. If it's 5 or more, round up. If it's 4 or less, round down.

For Extended Level, also know:

Rounding to a specific PLACE (nearest 10, 100, 1000) is common in real-life contexts.
Truncating is NOT rounding — it just chops off digits. Avoid unless explicitly asked.

Decimals

Short Study Notes in the form of Slides

Short Study Notes — Decimals

Detailed Notes

What you’ll learn

How it’s examined

1Add decimals with different d.p.

2Multiply decimals

3Divide decimals

4Round to d.p. and s.f.

Place value

Decimal place (d.p.)

Significant figure (s.f.)

Truncate

✕Adding decimals as if they were whole numbers, right-aligned.

✕Forgetting to count decimal places in the answer.

✕Counting leading zeros as significant figures.

Practice questions

Past paper style quiz

Assess your understanding

Decimals — frequently asked questions

Decimals

Short Study Notes in the form of Slides

Short Study Notes — Decimals

Detailed Notes

What you’ll learn

How it’s examined

1Add decimals with different d.p.

2Multiply decimals

3Divide decimals

4Round to d.p. and s.f.

Place value

Decimal place (d.p.)

Significant figure (s.f.)

Truncate

✕Adding decimals as if they were whole numbers, right-aligned.

✕Forgetting to count decimal places in the answer.

✕Counting leading zeros as significant figures.

Practice questions

Past paper style quiz

Assess your understanding

Decimals — frequently asked questions