Decimal Practice Questions

When adding decimals, align the decimal points vertically and add zeros as placeholders where necessary:

$$\begin{array}{rrcr}& 4& .& 560\\ +& 3& .& 789\\ & 8& .& 349\end{array}$$

Start by adding the thousandths column (\(0 + 9 = 9\)), then the hundredths column (\(6 + 8 = 14\), write 4 and carry 1), then the tenths column (\(5 + 7 + 1 = 13\), write 3 and carry 1), and finally the ones column (\(4 + 3 + 1 = 8\)).

When subtracting decimals, align the decimal points and add trailing zeros as placeholders:

$$\begin{array}{rrcr}& 9& .& 040\\ -& 3& .& 567\\ & 5& .& 473\end{array}$$

Since 0 is less than 7 in the thousandths place, you must borrow from the hundredths place. Continue borrowing as needed and subtract column by column from right to left.

When multiplying decimals, first multiply the numbers as if they were whole numbers:

\(6 \times 4 = 24\)

Then, count the total number of decimal places in both factors. 0.6 has one decimal place and 0.4 has one decimal place, for a total of two decimal places. Place the decimal point in the product so it has two decimal places:

\(0.6 \times 0.4 = 0.24\)

To divide by a decimal, first move the decimal point in the divisor to the right until it becomes a whole number. Move the decimal in the dividend the same number of places:

\(7.2 \div 0.9 = 72 \div 9 = 8\)

By multiplying both numbers by 10, you eliminate the decimals and can divide normally.

To round to the nearest tenth, look at the digit in the hundredths place. In 12.36, the hundredths digit is 6. Since the number is 5 or greater, round the tenths digit up:

\(12.36 \approx 12.4\)

To compare decimals, write each number with the same number of decimal places by adding trailing zeros:

0.305, 0.350, 0.300, 0.053

Now compare digit by digit from left to right. The correct order from least to greatest is:

0.053, 0.300, 0.305, 0.350

To find the total cost, add the two prices together. Align the decimal points and add column by column:

$$\begin{array}{rrcr}& 4& .& 79\\ +& 3& .& 48\\ & 8& .& 27\end{array}$$

Add the hundredths (\(9 + 8 = 17\), write 7 carry 1), then the tenths (\(7 + 4 + 1 = 12\), write 2 carry 1), then the ones (\(4 + 3 + 1 = 8\)).

First, multiply the numbers as if they were whole numbers (ignoring the decimals):

\(25 \times 314 = 7{,}850\)

Next, count the total number of decimal places in both factors. 2.5 has one decimal place and 3.14 has two decimal places, giving a total of three. Place the decimal point three places from the right in the product:

\(2.5 \times 3.14 = 7.850 = 7.85\)

To divide by a decimal, multiply both the dividend and divisor by 10 to eliminate the decimal in the divisor:

\(15.6 \div 1.2 = 156 \div 12 = 13\)

Now perform the division with whole numbers. Since \(12 \times 13 = 156\), the answer is 13.

To find the total time, add all three lap times. Align the decimal points:

$$\begin{array}{rrcr}& 2& .& 45\\ & 2& .& 38\\ +& 2& .& 57\\ & 7& .& 40\end{array}$$

Add the hundredths (\(5 + 8 + 7 = 20\), write 0 carry 2), then the tenths (\(4 + 3 + 5 + 2 = 14\), write 4 carry 1), then the ones (\(2 + 2 + 2 + 1 = 7\)).

Multiply the numbers as whole numbers first:

\(8 \times 5 = 40\)

Count the total decimal places: 0.08 has two decimal places and 0.05 has two decimal places, for a total of four. Place the decimal point four places from the right in the product:

\(0.08 \times 0.05 = 0.0040 = 0.004\)

First, find the total cost by multiplying the price of one notebook by 3:

\(\$2.75 \times 3 = \$8.25\)

Then, subtract the total cost from the amount paid:

$$\begin{array}{rrcr}& 20& .& 00\\ -& 8& .& 25\\ & 11& .& 75\end{array}$$

To divide by 0.08, multiply both numbers by 100 to make the divisor a whole number:

\(45.6 \div 0.08 = 4{,}560 \div 8\)

Now divide:

\(4{,}560 \div 8 = 570\)

To convert a fraction to a decimal, divide the numerator by the denominator:

\(3 \div 8 = 0.375\)

Perform the long division: 8 goes into 30 three times (remainder 6), 8 goes into 60 seven times (remainder 4), and 8 goes into 40 exactly five times.

To find the total amount of flour needed, multiply the amount per batch by the number of batches:

\(1.75 \times 2.5\)

Multiply as whole numbers first: \(175 \times 25 = 4{,}375\). Count the total decimal places: 1.75 has two and 2.5 has one, for a total of three. Place the decimal three places from the right:

\(1.75 \times 2.5 = 4.375 \text{ cups}\)