70.5
1) To divide a decimal number by another one, we can turn them into fractions and simplify it, whenever possible:
[tex]\begin{gathered} 6.345=\frac{6345}{1000} \\ 0.09=\frac{9}{100} \end{gathered}[/tex]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:
[tex]\frac{\frac{6345}{1000}}{\frac{9}{100}}=\frac{6345}{1000}\times\frac{100}{9}=\frac{6345}{90}=\frac{141}{2}=70.5[/tex]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.
