Evaluate. (a) $35 - 27.3$ \_\_\_\_\_\_ (b) $1.3 \times 0.03$ \_\_\_\_\_\_

Mathematics (Syllabus D) 4024/11 — October/November 2010

Cambridge O-Level · Non-calculator · worked solutions for every part, with the mark scheme

questions

marks

120

minutes

Topics Algebra and Graphs · Number · Geometry · Mensuration · Statistics · Coordinate Geometry · +4 more

Q1NumberFree sample

Evaluate.

(a)

$35 - 27.3$

______

DifficultyEasy

Worked solution

Approach

Rewrite $35$ as $35.0$ so both numbers have the same number of decimal places, then subtract.

Working

35.0 - 27.3 = 7.7

The mark scheme also accepts $7\frac{7}{10}$ , since $0.7 = \frac{7}{10}$ .

Answer

7.7

Final answer

7.7

Detailed explanation

Walkthrough

We need to evaluate $35 - 27.3$ . Write $35$ as $35.0$ so the decimal points line up. Subtracting $27.3$ from $35.0$ gives $7.7$ : $35.0 - 27.0 = 8.0$ , and $8.0 - 0.3 = 7.7$ . The mark scheme also accepts $7\frac{7}{10}$ because $0.7 = \frac{7}{10}$ .

Key Takeaways

Decimal subtraction requires aligning place values by the decimal point. A whole number can be written with a decimal point and zeros so that both numbers have the same number of decimal places.

Common Mistakes

Forgetting to borrow when subtracting across zeros.
Writing $8$ instead of $7.7$ by subtracting only the whole-number parts.
The mark scheme says the answer is $7.7$ or $7\frac{7}{10}$ only, so do not leave an unsupported or differently written value.

Things to Be Careful About

This is a non-calculator question, so the subtraction should be done by hand with the decimal points aligned. Give the exact value, not a rounded version.

Techniques used

align decimal pointssubtract using place valueexpress the result as a decimal or fraction

(b)

$1.3 \times 0.03$

______

DifficultyEasy

Worked solution

Approach

Multiply the numbers as whole numbers first, then place the decimal point using the total number of decimal places in the two factors.

Working

13 \times 3 = 39

$1.3$ has 1 decimal place and $0.03$ has 2 decimal places, so the product must have $1 + 2 = 3$ decimal places.

1.3 \times 0.03 = 0.039

Answer

0.039

Final answer

0.039

Detailed explanation

Walkthrough

First ignore the decimal points and multiply: $13 \times 3 = 39$ . Now count decimal places: $1.3$ has one digit after the decimal point and $0.03$ has two digits after the decimal point, so the product needs $1 + 2 = 3$ decimal places. Starting from $39$ , move the decimal point three places to the left, inserting a zero before the $3$ : $39 \to 3.9 \to 0.39 \to 0.039$ .

Key Takeaways

Multiplying decimals can be done by multiplying whole numbers and then adjusting the decimal point by the total number of decimal places. This avoids calculator errors.

Common Mistakes

Placing the decimal point incorrectly: $0.39$ or $0.0039$ are wrong.
Treating $0.03$ as $0.3$ and getting $0.39$ .
Forgetting the leading zero before the decimal point.

Things to Be Careful About

The mark scheme accepts equivalent forms (oe), but the standard exact answer is $0.039$ . On the non-calculator paper, show the by-hand multiplication and the decimal-point adjustment.

Techniques used

multiply integers ignoring decimal pointscount total decimal placesplace the decimal point in the product

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