Year 7 Decimals: free practice test with answers

Sample decimals questions with answers

Try each one before you open the answer.

1. Place value and decimals

   In the number $37.0592$, what is the value of:

   (a) the digit $9$

   (b) the digit $5$

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   Key idea: After the decimal point the places are tenths, hundredths, thousandths, ten-thousandths.

   1. Decimal places of $37.0592$: tenths $0$, hundredths $5$, thousandths $9$, ten-thousandths $2$
   2. (a) $9$ is in the thousandths place: $\dfrac{9}{1000} = 0.009$
   3. (b) $5$ is in the hundredths place: $\dfrac{5}{100} = 0.05$

   Answer: (a) $9$ thousandths ($0.009$) (b) $5$ hundredths ($0.05$)

2. Rounding decimals

   Round $47.3862$ to 2 decimal places.

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   Key idea: Look at the digit in the third decimal place to decide whether to round up or keep the second decimal place the same.

   1. The second decimal place digit is $8$.
   2. The third decimal place digit is $6$, which is $5$ or more, so round up.
   3. $47.3862$ rounded to 2 decimal places is $47.39$.

   Answer: $47.39$

3. Adding and subtracting decimals

   Calculate $15.4 - 7.86$.

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   Key idea: Line up the decimal points and fill empty places with zeros.

   1. $15.40 - 7.86$
   2. $= 7.54$

   Answer: $7.54$

4. Multiplying and dividing decimals by 10, 100, 1000 etc.

   Find $4.067 \times 100$.

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   Key idea: Multiplying by $100$ moves each digit two places to the left (the decimal point appears to move two places right).

   1. $100$ has $2$ zeros, so move the decimal point $2$ places right
   2. $4.067 \to 406.7$

   Answer: $406.7$

5. Multiplying decimals

   Priya is buying ribbon to decorate party bags. Each party bag needs 0.35 metres of ribbon. She is making 12 party bags. Ribbon costs $2.40 per metre. How much will the ribbon cost in total?

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   Key idea: First find the total length of ribbon needed by multiplying decimals, then multiply by the cost per metre.

   1. Find the total length: $0.35 \times 12$\

   $$0.35 \times 12 = 0.35 \times 10 + 0.35 \times 2 = 3.50 + 0.70 = 4.20 \text{ metres}$$

   2. Find the total cost: $4.20 \times 2.40$\

   $$4.20 \times 2.40 = 4.20 \times 2 + 4.20 \times 0.40 = 8.40 + 1.68 = 10.08$$

   3. The total cost is $10.08.

   Answer: $10.08

6. Dividing decimals

   Calculate $8.4 \div 0.7$.

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   Key idea: Multiply both numbers by $10$ so you divide by a whole number.

   1. $8.4 \div 0.7 = 84 \div 7$
   2. $= 12$

   Answer: $12$

7. Connecting decimals and fractions

   Write $\dfrac{7}{8}$ as a decimal.

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   Key idea: Divide the numerator by the denominator.

   1. $7 \div 8 = 0.875$

   Answer: $0.875$

8. Connecting decimals and percentages

   Write each decimal as a percentage: (a) $0.47$ (b) $0.6$ (c) $1.25$

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   Key idea: To change a decimal to a percentage, multiply by $100$.

   1. (a) $0.47 \times 100 = 47\%$
   2. (b) $0.6 \times 100 = 60\%$
   3. (c) $1.25 \times 100 = 125\%$

   Answer: (a) $47\%$ (b) $60\%$ (c) $125\%$

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 7 rounding and estimation worksheet
• Year 7 fraction operations worksheet
• Year 7 fractions and decimals worksheet
• Year 7 percentages worksheet