Dividing Whole Numbers by Decimals

1.1

420 ÷ 0.6

Solution

To get the divisor as w whole number we can multiply by  10  here.

420 ÷ 0.6  ×  10   =>   4200 ÷ 6

Now we can proceed and set up to perform the sum as long division.
\begin{array}{r} \\[-2pt] 6 {\bf{|}} {\overline{\space 4200. \space\space}} \end{array}

We place a decimal point at the end of the dividend number.
Because if we don’t get a full answer using long division before reaching the decimal point, any digits found after will be beyond a decimal point in the answer number.

\begin{array}{r} 0710\space \\[-2pt] 6 {\bf{|}} {\overline{\space 4260. }}\\ {\text{--}}\space \underline{42} \space\space\space\space\space \\ 06 \space\space\space\\ {\text{--}}\space \underline{6} \space\space\space \\ 00\space \\ {\text{--}}\space \underline{0}\space \\ 0\space \\ \end{array}
Here an answer is obtained before reaching the decimal point.

426 ÷ 0.6 = 710



1.2

87 ÷ 1.2

Solution

87 ÷ 1.2  ×  10   =>   870 ÷ 12

We can now proceed and set up to perform the sum as long division.

\begin{array}{r} 072.\space\space\\[-2pt] 12 {\bf{|}} {\overline{\space 870. \space\space}} \\ {\text{--}}\space \underline{84} \space\space\space\space\space \\ 30 \space\space\space\\ {\text{--}}\space \underline{24} \space\space\space \\ 6 \space\space\space \\ \end{array}

At this point we will proceed beyond the decimal point with long division.

We place an extra zero to bring down in the dividend, this doesn’t change the overall value as the zero is beyond the decimal point.
Along with also placing a decimal point in the answer section in the relevant position above the dividend.

\begin{array}{r} 072.5\space\\[-2pt] 12 {\bf{|}} {\overline{\space 870.0 \space}} \\ {\text{--}}\space \underline{84} \space\space\space\space\space\space \\ 30 \space\space\space\space\\ {\text{--}}\space \underline{24} \space\space\space\space \\ 6\space0\space \\ {\text{--}}\space \underline{6\space0}\space \\ 0\space \\ \end{array}

87 ÷ 1.2 = 72.5



1.3

328 ÷ 0.05

Solution

Here a multiplication of  100  will make the divisor a whole number.

328 ÷ 0.05  ×  100   =>   32800 ÷ 5

We can now proceed and set up to perform the sum as long division.

\begin{array}{r} 06560\space\space\\[-2pt] 5 {\bf{|}} {\overline{\space 32800. \space}} \\ {\text{--}}\space \underline{30} \space\space\space\space\space\space\space\space \\ 28 \space\space\space\space\space\space\\ {\text{--}}\space \underline{25} \space\space\space\space\space\space \\ 30\space\space\space\space \\ {\text{--}}\space \underline{30}\space\space\space\space \\ 00\space\space \\ {\text{--}}\space \underline{0}\space\space \\ 0\space\space \\ \end{array}

328 ÷ 0.05 = 6560



1.4

46 ÷ 0.7

Solution

46 ÷ 0.7  ×  100   =>   460 ÷ 7

We can now proceed and set up to perform the sum as long division.

\begin{array}{r} 065.714\space\\[-2pt] 7 {\bf{|}} {\overline{\space 460.000 \space}} \\ {\text{--}}\space \underline{42} \space\space\space\space\space\space\space\space\space\space \\ 40 \space\space\space\space\space\space\space\space\\ {\text{--}}\space \underline{35} \space\space\space\space\space\space\space\space \\ 5\space0\space\space\space\space\space \\ {\text{--}}\space \underline{4\space9}\space\space\space\space\space \\ 10\space\space\space \\ {\text{--}}\space \underline{7}\space\space\space \\ 30\space \\ \end{array}

Sometimes when dividing by decimal numbers the answer doesn’t terminate.

At the point we’ve reached it’s fine to round the answer to 2 decimal places.

46 ÷ 0.7 = 65.71