A number system muNote uses symbol Do Re Mi Fa So La Ti with

A number system muNote uses symbol Do, Re, Mi, Fa, So, La, Ti with equivalent decimal weight 0, 1, 2, 3, 4, 5, 6 respectively. In that case, answer the following. What is the decimal equivalent of ReDoLaTiLaSo? What is muNote equivalent of decimal number 987654321?

Solution

1. a) When we convert Munote which is 7 digit number system to decimal which is 10 digit number system. we use below formula

first 7 place decimal equivaluent of ReDoLaTiLaSo = 105654

Now we have to use below formula to convert this into decimal system

Decimal number = (left most digit in Munote * numbers of Munotes(7)^( Number of count of digit from right most (5)+ so on

so in expression

Decimal Number =
1*7^5+
0*7^4+
5*7^3+
6*7^2+
5*7^1+
4*7^0
=1*16807+0+5*343+6*49+5*7+4
=16807+0+1715+294+35+4
18855

2. we have to follow below process to get Munote equivalent of decimal number 987654321

First we have devide the decimal number by 7 and get the quotient and reminder and do as below.

987654321/7, here reminder is 3

141093474/7 reminder

20156210 4/7, 43

2879458 R 4, 443

411351 R 1, 1443

58764 R 3, 31443

8394 R 6, 631443

1199 R 1, 161443

171 R 2, 2161443

24 R 3, 32161443

3 R 3, 332161443

So the number in Munote is =3332161443