Decimals questions with answers

Questions

1. Question 1Add and subtract decimals

   Calculate $3.52 + 6.481$.

   Show the worked solution

   1. Step 1: Line up the decimal points: fill the empty places with zeros$3.520 + 6.481$
   2. Step 2: Add column by column, carrying where needed$= 10.001$
2. Question 2Multiply decimals

   Without using a calculator, find the value of $0.4 \times 0.9$.

   Show the worked solution

   1. Step 1: Multiply the numbers as if there were no decimal points$4 \times 9 = 36$
   2. Step 2: The answer has as many decimal places as the two numbers togetherDecimal places: $1 + 1 = 2$$0.4 \times 0.9 = 0.36$
3. Question 3Divide by a decimal

   Without using a calculator, find the value of $1.035 \div 0.9$.

   Show the worked solution

   1. Step 1: Multiply both numbers by the same power of 10 so that you divide by a whole number$1.035 \div 0.9 = 10.35 \div 9$
   2. Step 2: Divide (short division)$= 1.15$
4. Question 4Fraction to decimal

   Express $\dfrac{5}{16}$ as a decimal.

   Show the worked solution

   1. Step 1: Make the denominator a power of 10: multiply the top and the bottom by the same number$\dfrac{5}{16} = \dfrac{5 \times 625}{16 \times 625}$$= \dfrac{3125}{10000}$
   2. Step 2: Divide by the power of 10: move the decimal point one place to the left for each zero$= 0.3125$
5. Question 5Decimal to fraction

   Express $0.96$ as a fraction in its simplest form.

   Show the worked solution

   1. Step 1: Write it as a fraction over a power of 10 (one zero for each decimal place)$0.96 = \dfrac{96}{100}$
   2. Step 2: Divide the top and the bottom by their HCF$= \dfrac{96 \div 4}{100 \div 4}$$= \dfrac{24}{25}$
6. Question 6Terminating or recurring?

   Without dividing, state whether $\dfrac{11}{40}$ is a terminating decimal or a recurring decimal.

   Show the worked solution

   1. Step 1: Write the denominator as a product of prime factors$40 = 2^{3} \times 5$
   2. Step 2: A fraction in its simplest form is a terminating decimal only if its denominator has no prime factors other than 2 and 5The denominator has no prime factor other than $2$ and $5$, so $\dfrac{11}{40}$ is a terminating decimal.