Operations with Decimals

Given the decimal 12.45, the position for each number is defined below.

The decimal number 3.4512 has 3 as its whole number component and 0.4512 as its fractional part.

There are four decimal places here since there are four digits after the decimal point.

Use long division to convert $\frac{7}{8}$into a decimal.

Therefore, $\frac{7}{8}=0.875$

Convert 45% to a decimal.

Moving two spaces to the left, we obtain 45% = 0.45

Convert 3.67% to a decimal.

Moving two spaces to the left from the decimal point, we obtain 3.67% = 0.0367

Add 5.7 and 8.9

$5.7+8.914.6$

Subtract 2.3 from 4.8

$4.8-2.32.5$

Add 6 and 4.3

$6.\mathbf{0}+4.310.3$

Subtract 5 from 9.2

$9.2-5.\mathbf{0}4.2$

Add 5.43 and 6.678

$5.43\mathbf{0}+6.67812.108$

Subtract 2.3456 from 4.1

$4.1\mathbf{000}-2.34561.7544$

Multiply 3.6 by 2.3

Ignoring the decimal places, we obtain 36 × 23 = 826.

Both decimals, 3.6 and 2.3 have one decimal place each.

The sum of these decimal places is two.

Thus, the product of 36 × 23 = 826 must have two decimal places.

Putting in the decimal point, we obtain 3.6 × 2.3 = 8.26.

Multiply 5.7 by 8

Ignoring the decimal places, we obtain 57 × 8 = 456.

The decimal 5.7 has one decimal place while the whole number 8 has no decimal place.

The sum of these decimal places is one.

Thus, the product of 57 × 8 = 456 must have one decimal place.

Putting in the decimal point, we obtain 5.7 × 8 = 45.6.

Multiply 2.165 by 9.1

Ignoring the decimal places, we obtain 2165 × 91 = 197015.

The decimals 2.165 and 9.1 have 3 decimal places and one decimal place respectively.

The sum of these decimal places is four.

Thus, the product of 2165 × 91 = 197015 must have four decimal places.

Putting in the decimal point, we obtain 2.165 × 9.1 = 19.7015.

Multiply 3.87 by 100

There are two zeros in the number 100, so we must shift the decimal point of 3.87 to two places to the right.

3.87 × 100 = 387

Multiply 7.3956 by 1000

There are three zeros in the number 1000, so we must shift the decimal point of 7.3956 three places to the right.

7.3956 × 1000 = 7395.6

Divide 4.62 by 0.12

Here, we have 4.62 ÷ 0.12 where the dividend is 4.62 and the divisor is 0.12.

To change the divisor into a whole number, we multiply it by 100. This yields 0.12 × 100 = 12.

Multiplying this same value to the dividend, we obtain 4.62 × 100 = 462.

Thus, we have 462 ÷ 12 which is the same as 4.62 ÷ 0.12.

Conducting long division, we obtain

Thus, 4.62 ÷ 0.12 = 38.5.

Divide 5.525 by 5

Here, we have 5.525 ÷ 5 where the dividend is 5.525 and the divisor is 5.

The divisor is already in the form of a whole number. However, the dividend is still in the form of a decimal.

To tackle this problem, we shall conduct long division while ignoring the decimal point of the dividend.

We shall now place the decimal point of the answer directly above the decimal point of the dividend as below.

Thus, 5.525 ÷ 5 = 1.105.

Divide 3.432 by 1.04

Here, we have 3.432 ÷ 1.04 where the dividend is 3.432 and the divisor is 1.04.

To change the divisor into a whole number, we multiply it by 100. This yields 1.04 × 100 = 104.

Multiplying this same value to the dividend, we obtain 3.432 × 100 = 343.2.

Thus, we have 343.2 ÷ 104 which is the same as 3.432 ÷ 1.04.

Although the divisor is already in the form of a whole number, the dividend is still in the form of a decimal.

As before, we shall conduct long division while ignoring the decimal point of the dividend.

We shall now place the decimal point of the answer directly above the decimal point of the dividend as below.

Thus, 3.432 ÷ 1.04 = 3.3.

Divide 2.34 by 10

There is one zero in the number 10, so we must shift the decimal point of 2.34 one place to the left.

2.34 ÷ 10 = 0.234.

Divide 17635.6 by 1000

There are three zeros in the number 1000, so we must shift the decimal point of 17635.6 three places to the left.

17635.6 ÷ 1000 = 17.6356

Evaluate$0.123-4.5\%$.

Solution

We begin by converting the percentage term

4.5% = 4.5 ÷ 100 = 0.045

We can now perform subtraction as usual

$0.123-0.0450.078$

Thus, the final answer is 0.078

Evaluate $\frac{3}{4}+0.57$.

Solution

We begin by converting the fraction term

$\frac{3}{4}=3÷4=0.75$

We can now perform addition as usual

$0.75+0.571.32$

Thus, the final answer is 1.32

Evaluate$(2.45+0.72)\times 3.12-1.99$.

Solution

We shall first calculate the expression inside the parenthesis

$$\begin{gathered} 2.45+0.723.17 \\ 3.17\times 3.12-1.99 \end{gathered}$$

Next, we shall conduct multiplication

$$\begin{gathered} 3.17\times 3.12=9.8904 \\ 9.8904-1.99 \end{gathered}$$

Finally, we shall perform subtraction

$9.8904-1.99007.9004$

Thus, the final answer is 7.9004.

Evaluate$4.6+\frac{1.3-0.7}{0.4}-2.3$.

Solution

We shall first calculate the expression in the grouping

$$\begin{gathered} \frac{1.3-0.7}{0.4}=(1.3-0.7)÷0.4=0.6÷0.4=1.5 \\ 4.6+1.5-2.3 \end{gathered}$$

Next, we shall conduct addition

$$\begin{gathered} 4.6+1.56.1 \\ 6.1-2.3 \end{gathered}$$

Finally, we shall perform subtraction

$6.1-2.33.8$

Thus, the final answer is 3.8.

Evaluate $0.3^2+(3.4-2.1)÷1.6$.

Solution

We shall first calculate the expression inside the parenthesis

$$\begin{gathered} 3.4-2.11.3 \\ 0.3^2+1.3÷1.6 \end{gathered}$$

Next, we shall derive the exponent

$$\begin{gathered} 0.3^2=0.3\times 0.3=0.09 \\ 0.09+1.3÷1.6 \end{gathered}$$

Following this, we shall conduct division

$$\begin{gathered} 1.3÷1.6=0.8125 \\ 0.09+0.8125 \end{gathered}$$

Finally, we shall conduct addition

$0.0900+0.81250.9025$

Thus, the final answer is 0.9025.