Question

Show me how do divided 6.345 ÷ 0.09 step by step.

Answer 1

70.5

1) To divide a decimal number by another one, we can turn them into fractions and simplify it, whenever possible:

`\begin{gathered} 6.345=(6345)/(1000) \\ 0.09=(9)/(100) \end{gathered}`

Each decimal place represents the number of zeros beside the 1 on the denominator, or each decimal place represents 1/10.

2) Dividing it as fractions, we need to multiply the first by its reciprocal:

`((6345)/(1000))/((9)/(100))=(6345)/(1000)*(100)/(9)=(6345)/(90)=(141)/(2)=70.5`

Notice that we simplified 6345/90 by 45 then we got 141/2. In other words, 6345/100 and 141/2 are the same, Because 141/2 is the nonreducible fraction.

To divide 6.345 ÷ 0.09 using long division, let's multiply first both numbers by 100, doing this we'll keep the proportionality, and make our calculations easier.

6.345 x 100 = 634.5

0.09 x 100 = 9

1) First, let's divide 634 by 9. 70 x 9 = 630. The closest value.

2) Then let's bring down 4.5. 4.5 ÷ 9 = 0.5

3) 70.5 x 9 = 634.5.